document.write( "Question 1030558: verify that if an integer is simultaneously a square and a cube then it must beveither of the form 7k or 7k+1. \n" ); document.write( "

Algebra.Com's Answer #645439 by richard1234(7193) $\"\"$ $\"About$

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If the integer is a square and a cube, then it must be a 6th power of some integer x.\r
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\n" ); document.write( "\n" ); document.write( "If x is a multiple of 7, then

is a multiple of 7 and is equal to 7k for some integer k. Otherwise, x and 7 are relatively prime, and by Fermat's little theorem, we have

, which is equivalent to saying

for some integer k. \n" ); document.write( "

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