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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: May 2016
1/x + 1/y = 1/z, (x, z) = 1
Let be positive integer for which , Prove that , and are all squares … Continue reading
a^4 + 2n(ab)^2 + b^4 = c^4 + 2n(cd)^2 + d^4 …. Part 2
for n = 1, 2, 3, …, 10 For n = 11, 12, 13, …, 100 … Continue reading
a^4 + 14(a*b)^2 + b^4 = c^4 + 14(c*d)^2 + d^4
I like this type of equations, because they can be used to form identities. Let’s solve for n = 7 where are distinct positive integers For example, Note that So, … Continue reading
Equation : x^2 + y^3 = z^4
Determine the next values. Establish the recurrence relation.
A^2 + B^2 + C^2 = D^2 + E^2
Also true is, Let Let’s take all primitive Pythagorean triples with , for n = 1 … Continue reading
When x^2 + p*y and y^2 + p*x are squares, p is a small odd prime
Find positive integers so that the expressions , and are to made squares where p = 3, 5, 7, 11, 13, 17, 19 … Continue reading
(a^2 + b^2 + c^2 + d^2)(p^2 + q^2 + r^2 + s^2) — Part 3
[ a sum of four squares] Or [ as a sum of seven squares ] Can you find positive integers so that the expressions are to be made squares. … Continue reading
(a*p + b*q + c*r), (a*q – b*p), (a*r – c*p), (b*r – c*q) — Part 2
Can you find positive integers so that the expressions are to be made squares. Note that … Continue reading
When a*b + c*d, a*d – b*c are squares — Part 1
Can you find positive integers so that the expressions are to be made squares Note that I want to produce For example, …….. ……… …….. … Continue reading
a^2 + ab + b^2 = c^2 + cd + d^2; a^4 + (ab)^2 + b^4 = c^4 + (cd)^2 + d^4
or equivalently, that is, For example, for example,