document.write( "Question 814632: if 3^(8n+3) divided by 5 what will be the remainder,where n is a integer
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Algebra.Com's Answer #515304 by Edwin McCravy(20056) $\"\"$ $\"About$

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if 3^(8n+3) divided by 5 what will be the remainder,where n is a integer
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document.write( "If n=1, we have  =  = 177147, when divided by 5, has remainder 2.\r\n" );
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document.write( "That is \r\n" );
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document.write( "We will try to prove, by induction, that the remainder will always be 2.\r\n" );
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document.write( "That is, we will try to prove  for some integer p\r\n" );
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document.write( "Assume that for all , \r\n" );
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document.write( "(1)       for some integer p       <--assumed\r\n" );
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document.write( "we want to use (1) to prove: \r\n" );
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document.write( "          for some integer q   <--unproved \r\n" );
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document.write( "or\r\n" );
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document.write( "          for some integer q     <--unproved\r\n" );
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document.write( "or\r\n" );
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document.write( "(2)      for some integer q       <--unproved\r\n" );
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document.write( "We want to show that the assumption of (1) imples (2)\r\n" );
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document.write( "Multiply both sides of (1) by 3^8\r\n" );
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document.write( "        \r\n" );
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document.write( "        \r\n" );
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document.write( "         \r\n" );
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document.write( "So we take integer  and we have proved (2)\r\n" );
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document.write( "(2)      for some integer q\r\n" );
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document.write( "Therefore the remainder is 2 for all n\r\n" );
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document.write( "Edwin

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