document.write( "Question 889703: Prove that for any positive integer n, the value of the expression 3^(2n+2)-8n-9 is divisible by 64 \n" ); document.write( "

Algebra.Com's Answer #538785 by richard1234(7193) $\"\"$ $\"About$

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We induct on n. n = 1 is trivial (3^4 - 8 - 9 = 64).\r
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\n" ); document.write( "\n" ); document.write( "Assume

for some integer

. Then

.\r
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\n" ); document.write( "\n" ); document.write( "We want to show that

. This is equivalent to showing that

. However, since we know that

, the statement we wish to prove is equivalent to

, which is true since the LHS equals

. The induction is complete and the statement holds for all positive integers n. \n" ); document.write( "

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