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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
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 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: August 2016
When {(x+y+z)^5x, (x+y+z)^5y, (x+y+z)^5z} are squares
Find integers such that , , are squares, where … Continue reading
Three numbers in A.P. whose sum is a 6th power
Find three numbers in arithmetical progression whose sum is a 6th power.
1 + x + … + x^m = 1 + y + … + y^n
It appears that for holds only for in addition to evident solutions if or is negative. … Continue reading
Pell identities: (P(n))^4+(P(n+1))^4+(P(n+2))^4 = 2((P(n))^2+2P(n)P(n+1)+4(P(n+1))^2)^2
Prove the following identities: Let and be any real numbers Then can be confirmed algebraically. This identity has an interesting application to the Pell family. Let be an integer … Continue reading
Powers of 2 and 3 as a sum of two powers
and so on. and so on. and so on.
Primitive Pythagorean triples (a, b=a+1, c)
Let P be the perimeter (1) Can you explain the following: The generators and of the first few triangles are the Pell numbers 2, 5, 12, 29, …, … Continue reading
Make {x^2 + y^2 + z^2, x^2 y^2 + x^2 z^2 + y^2 z^2} squares – Part 2
Find three positive integers to can make the two expressions squares Here’s a parametric solution established by Euler: In two ways: … Continue reading
Make {x^2 + y^2 + z^2, x^2 y^2 + x^2 z^2 + y^2 z^2} squares — Part 1
Find three positive integers to can make the two expressions squares Here are some solutions: … Continue reading
Make {2x^2 + y^2 + z^2, x^2 + 2y^2 + z^2, x^2 + y^2 + 2z^2} squares
Find three positive integers to can make the three expressions squares Can you find three distinct positive integers that satisfy the system of equations? … Continue reading