
Lonely Runner Fortification
How much would we have to fortify the Lonely Runner problem in order to find a counterexample speed assignment, by adding extra runners, while keeping the loneliness criteria the same? For N Runners,
How much would we have to fortify the Lonely Runner problem in order to find a counterexample speed assignment, by adding extra runners, while keeping the loneliness criteria the same? For N Runners,

By
Lee Morgenstern
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base 2 factoring algorithm
I use my base 2 factoring algorithm to confirm that 31 is prime. z = 31 z = (1 + 2 + 4 + 8 + 16) = (1 + 2 * x1 + 4 * x2) * (1 + 2 * y1 + 4 * y2 + 8 * y3 + 16 * y4) 1 + 2*(x1 + y1) + 4*(x2+x1*y1+y2) +
I use my base 2 factoring algorithm to confirm that 31 is prime. z = 31 z = (1 + 2 + 4 + 8 + 16) = (1 + 2 * x1 + 4 * x2) * (1 + 2 * y1 + 4 * y2 + 8 * y3 + 16 * y4) 1 + 2*(x1 + y1) + 4*(x2+x1*y1+y2) +

By
Kermit Rose
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base 2 factoring
Today I thought of this alternative base 2 analysis of factoring. The number of steps to find the divisors should be a function of the logarithm of the number for which we wish to find the divisors, b
Today I thought of this alternative base 2 analysis of factoring. The number of steps to find the divisors should be a function of the logarithm of the number for which we wish to find the divisors, b

By
Kermit Rose
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Conjecture about primes 4 messages
Hi All Here is a conjecture about primes. All primes p from 2 to 113 can be written as p=x*(x+k)+c or p=x*(x+k)c where k is either 0 or 1 and c is either 1,2,3. The prime 127 is the first exception t
Hi All Here is a conjecture about primes. All primes p from 2 to 113 can be written as p=x*(x+k)+c or p=x*(x+k)c where k is either 0 or 1 and c is either 1,2,3. The prime 127 is the first exception t

By
kimowww
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Relating tables of addition to multiplication
Using the integers 0 through 3, you can make a table of addition. 0 1 2 3 This corresponds to (2^4  1) = (2^0 + 2^1) * (2^0 + 2^2) You cannot make a corresponding addition table using integers 0 thro
Using the integers 0 through 3, you can make a table of addition. 0 1 2 3 This corresponds to (2^4  1) = (2^0 + 2^1) * (2^0 + 2^2) You cannot make a corresponding addition table using integers 0 thro

By
Kermit Rose
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Puzzle 7 messages
Hi All I have an idea for a puzzle. The idea is to place the numbers from 1 to N^2 in a N*N square and note the general distance from k to k+1 in terms of x coordinates and y coordinates. The first nu
Hi All I have an idea for a puzzle. The idea is to place the numbers from 1 to N^2 in a N*N square and note the general distance from k to k+1 in terms of x coordinates and y coordinates. The first nu

By
kimowww
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formula for a product equal to the sum of two products
The following algebraic identity shows a deeper relationship between addition and multiplication. (q1+t2*t1*q2)*((t3 * t2+1) * q2) = (q1*q2) + (t2*q2) * (t3*t2*t1*q2 + t3*q1 + t1*q2) It is a formula f
The following algebraic identity shows a deeper relationship between addition and multiplication. (q1+t2*t1*q2)*((t3 * t2+1) * q2) = (q1*q2) + (t2*q2) * (t3*t2*t1*q2 + t3*q1 + t1*q2) It is a formula f

By
Kermit Rose
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FW: RE: [UnsolvedProblems] Puzzle
Original Message From: "kermit@..." <kermit@...> Sent: Saturday, November 12, 2022 6:40pm To: yahoo.com@groups.io Subject: FW: RE: [UnsolvedProblems] Puzzle Kim, what would be the score for
Original Message From: "kermit@..." <kermit@...> Sent: Saturday, November 12, 2022 6:40pm To: yahoo.com@groups.io Subject: FW: RE: [UnsolvedProblems] Puzzle Kim, what would be the score for

By
Kermit Rose
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FW: Re: [UnsolvedProblems] Puzzle
Hello Kim. If I understand your puzzle correctly, there is probably a trivial solution for any order square. For the 4 by 4 square, I submit 7 8 9 10 6 1 2 11 5 4 3 12 16 15 14 13 Kermit Original
Hello Kim. If I understand your puzzle correctly, there is probably a trivial solution for any order square. For the 4 by 4 square, I submit 7 8 9 10 6 1 2 11 5 4 3 12 16 15 14 13 Kermit Original

By
Kermit Rose
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FW: Re: [UnsolvedProblems] From prime integers to prime polynomials: Fixing typo
Hello Daniel. You are correct. An example of your point is (a * x^2  b*x + c) * (a * x^2 + b*x + c) = (a* x^2 + c)^2  b^2 * c*2 = a^2 * x^4 + (2 * a * c  b^2) * x^2 + c^2 a*x^2  b*x + c = 1 a*x^2
Hello Daniel. You are correct. An example of your point is (a * x^2  b*x + c) * (a * x^2 + b*x + c) = (a* x^2 + c)^2  b^2 * c*2 = a^2 * x^4 + (2 * a * c  b^2) * x^2 + c^2 a*x^2  b*x + c = 1 a*x^2

By
Kermit Rose
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From prime integers to prime polynomials 3 messages
3 = 2+1 implies that x+1 is irreducible. 5 = 2^2 + 1 implies that x^2+1 is irreducible. 7 = 2^2+2+1 implies that x^2 + x + 1 is irreducible. 11 = 2^3 + 2 + 1 implies that x^3 + x + 1 is irreducible. 1
3 = 2+1 implies that x+1 is irreducible. 5 = 2^2 + 1 implies that x^2+1 is irreducible. 7 = 2^2+2+1 implies that x^2 + x + 1 is irreducible. 11 = 2^3 + 2 + 1 implies that x^3 + x + 1 is irreducible. 1

By
Kermit Rose
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Can numbers of this form be parametrized ? 8 messages
Hi all Can numbers of this form be parametrized ? where x,z,r and Q are integers and x is odd. More specifically I want to know if there are infinetely many odd integers W which is not equal to any nu
Hi all Can numbers of this form be parametrized ? where x,z,r and Q are integers and x is odd. More specifically I want to know if there are infinetely many odd integers W which is not equal to any nu

By
kimowww
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factoring by addition table
Introducing the ordered lists: How is an ordered list, [0, 1, 2, 3], made into a puzzle? The addition operation is defined on the ordered lists. Addition Table [0,1] [0,2] [0,1,2] [0,3] [0,1] [0,3] [0
Introducing the ordered lists: How is an ordered list, [0, 1, 2, 3], made into a puzzle? The addition operation is defined on the ordered lists. Addition Table [0,1] [0,2] [0,1,2] [0,3] [0,1] [0,3] [0

By
Kermit Rose
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Hi All, I'm back
Hi All, I'm back. Finally a more simple and clear proof for Fermat the last (I hope) was found with my CMA. From Sum to Step Sum, then to the limit where only the integral can arrive from n=3. Here th
Hi All, I'm back. Finally a more simple and clear proof for Fermat the last (I hope) was found with my CMA. From Sum to Step Sum, then to the limit where only the integral can arrive from n=3. Here th

By
Stefano Maruelli
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ring of number lists 12 messages
The ring of (lists of numbers). Define a (list of numbers) to be a list of numbers, [a1, a2, a3, ...] An equivalent term for (list of numbers) is number list. Define the sum of two number lists, [a1,
The ring of (lists of numbers). Define a (list of numbers) to be a list of numbers, [a1, a2, a3, ...] An equivalent term for (list of numbers) is number list. Define the sum of two number lists, [a1,

By
Kermit Rose
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Factoring 4 messages
Re factoring algorithms: a good test is that they have to be able to easily factor 20+ digit numbers, since the simplest sieve methods can handle these in less than a millisecond. Tim
Re factoring algorithms: a good test is that they have to be able to easily factor 20+ digit numbers, since the simplest sieve methods can handle these in less than a millisecond. Tim

By
Tim Roberts
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RSA ; List number factoring
How can I apply the concept of list number factorization to factor large numbers? I thought I should study examples where I knew the factors. Perhaps some principles of deriving the factors would emer
How can I apply the concept of list number factorization to factor large numbers? I thought I should study examples where I knew the factors. Perhaps some principles of deriving the factors would emer

By
Kermit Rose
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Factoring by addition table 3 messages
Factoring by Addition Table Transform lists by replacing an integer by 2 copies of the next smaller integer. Equate integer to list via exponents in base 2 representation. 9 = [0,3] = [0,2,2] = [0,1,1
Factoring by Addition Table Transform lists by replacing an integer by 2 copies of the next smaller integer. Equate integer to list via exponents in base 2 representation. 9 = [0,3] = [0,2,2] = [0,1,1

By
Kermit Rose
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Progress in factoring algorithm 3 messages
Hello friends. The attached Excel file applies the mod 24 factoring algorithm that I developed today. If z is prime, or if the smallest divisor > 1 is less than 24, p = 0 finds the factors. If z is co
Hello friends. The attached Excel file applies the mod 24 factoring algorithm that I developed today. If z is prime, or if the smallest divisor > 1 is less than 24, p = 0 finds the factors. If z is co

By
Kermit Rose
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Question 5 messages
Hi All Suppose we have 5 different elements which we will put in to a ordered list of 3 elements. In how many ways can this be done ? If repetitions are allowed then the answer is 5*5*5=5^3=125 Now wh
Hi All Suppose we have 5 different elements which we will put in to a ordered list of 3 elements. In how many ways can this be done ? If repetitions are allowed then the answer is 5*5*5=5^3=125 Now wh

By
kimowww
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