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Tag Archives: Equation
(x^2 – 1) (y^2 – 1) = (z^2 – 1)^2
An alternate form assuming , and are positive: or Here are the first few solutions: … Continue reading
Equation : (x – y)^n = x*y
Find triplets (x, y, n) of positive integers such that Note that if we set Hence and, … Continue reading
(x + y)(x + y + 1) = k*x*y
An interesting case of when 81, 289, 625, 1089, … are of the form … Continue reading
(1+x)(1+x^2) = y^2
Find all integers such that is a perfect square. Here are the first few solutions: , , , , Any other solutions? … Continue reading
tan A = tan B + tan C + tan D
Find other 4tuples of distinct integers between and that satisfy the relation Other solutions: How many such equations can you produce if we allow repeated angles? … Continue reading
a^4 + 14 a^2 b^2 + b^4 = c^4 + 14 c^2 d^2 + d^4
Find distinct positive integers such that Note that implies Using Paul’s first few solutions:
System : {6(x^2 – y^2), 10(x^2 + y^2)}
Give integral solutions
(A*B*C) (A^2 + B^2 + C^2) = (D*E*F) (D^2 + E^2 + F^2)
Find six distinct positive integers such that
(ab)(a + b)(a^2 + ab + b^2) = (cd)(c + d)(c^2 + cd + d^2)
where are integers Here’s one solution: Note that