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N = 5K , K IS +VE INTIGER,

5K = P^2Q ie either p or q .............or both could be a multiple of 5

for any p.q combination to be a multiple of 25

we have to satisfy the assumption (either p or q .............or both could be a multiple of 5) through its worst case scenario which is only q or only p is a multiple of five thus we need a square of each at least to make sure that we will end up with a 25 multiple

thus p^2*q^2 satisfies the worst case scenario



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