Squares from non squares...
Number Theory
Level
3
What is the sum of the lowest two non-square distinct positive integers, that can each be multiplied by the same third positive integer to give two different square numbers?
The answer is 10.
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1 solution
In order for two positive integers to be able to be made into a perfect square by multiplying them both by the same positive integer, the parities of the exponents of the prime factors needs to match.
The lowest two distinct positive integers that fit the bill are 2 and 8 .
2 + 8 = 1 0