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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Monthly Archives: November 2016
3 x 3 magic square w/ entries are distinct integer squares
….. ….. ….. ….. ….. ….. is a magic square, Can you find a number such that ——————————————– … Continue reading
Integer n such that 2*n^2 can be written as sum of two squares in four ways
Find the least integer such that can be written as sum of two squares in four ways Also, find the next few ones. Find the least integer such that … Continue reading
4X4 grid – gcd from 1 to 24
To place distinct integers in a n × n grid such that all gcds from 1 to 2*n(n1) are generated. If n = 4, then find 16 integers such … Continue reading
3X3 grid – gcd from 1 to 12
To place distinct integers in a n × n grid such that all gcds from 1 to 2*n(n1) are generated. If n = 3, then find 9 integers such that all gcds from 1 … Continue reading
Integers (a,b,c,d); each pairwise sum & sum of all four is a square
Find four integers such that are all squares The first few solutions are: Also found by pipo … Continue reading
Pythagorean triangle {a+b+c, a^2+b+c, a+(b+c)^2} are to made squares
Find a Pythagorean triangle such that are all squares … Continue reading
Diophantine equation : y^2 – p = 2^n, where p is a prime number
The diophantine equation where is a prime number < 100 The only solutions to the diophantine equation with y > 0 are given by (n, y) = … Continue reading
Diophantine equation : 2^a + 2^b + 2^c = x^2
Consider the Diophantine equation : for nonnegative integers,
Diophantine equation : (ab)/(a+b) + (bc)/(b+c) + (cd)/(c+d) + (da)/(d+a) = 0
Determine integral solutions of the Diophantine equation where are distinct Solutions: , , If , then , If , then , … Continue reading