Only one solution?
How many solutions are possible for 2 distinct positive integers and such that ?
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1 solution
2x2x2x2 = 4x4 For any distinct numbers a and b, (i) both are prime. If a^b = b^a, a| a^b => a |b^a, contradiction. (ii) one of them is a prime (as is the case with our solution pair, 2 and 4) 2 being an even prime, we arrive at 2^4 = 4^2, For any other prime (p) and non-prime numbers, p^n = n^p leads to n = p^k. or n = p*p2 *p3 and so on. This contradicts p being prime!