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-5^4 + 5^5 + 5^n and 2^4 + 2^7 + 2^n perfect squares

Source: Greek national M.O. 1995, Final Round, problem 1

November 20, 2011
number theory unsolvednumber theory

Problem Statement

Find all positive integers nn such that āˆ’54+55+5n-5^4 + 5^5 + 5^n is a perfect square. Do the same for 24+27+2n.2^4 + 2^7 + 2^n.
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