Anonymous

26. 1 and all of the even integers between 1 and 50 inclusive.

Anonymous

If p is a prime factor of n which occurs as pᵐ in n then it occurs as pᵐⁿ in nⁿ. For nⁿ to be a square mn must be divisible by 2 for all possible p. ∴ 2|n (n is even) (25) or 2|m for every prime factor (n is a square) (4)

Anonymous

Ans. all n in [1, 50] such that n is even or n= 1. Proof: 1^1=1^2=1. For the others, let n=2m, where m is in [1, 25], then n^n=[(2m)^m]^2 is a square number. e.g n=8=>8^8=(8^4)^2=4096^2=16777216 is a square number.