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CTK Exchange
shivgaur
Member since Mar-9-11
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Mar-20-11, 11:29 AM (EST) |
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"Number theory question"
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The Problem: Suppose for a positive integer n both 5n+1 and 7n+1 are perfect squares. Show that n is divisible by 24My attempt: Since 5n+1 is a perfect square and n is a positive integer then, the n's for which 5n+1 is a perfect square are: n= 3, 7, 16, 24 .......... and for 7n+1 : n = 5, 9, 24...... therefore the least common 'n' which makes both 5n+1 and 7n+1 a perfect square is 24 and therefore 'n' is divisible by 24. Any better approach to this problem?
Shiv |
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