document.write( "Question 1152069: Given 2;5;8 as a sequence prove that none of the terms are not a perfect
\n" ); document.write( "square \n" ); document.write( "

Algebra.Com's Answer #773986 by ikleyn(52803) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "Given 2, 5, 8 as a sequence. Prove that none of the terms $\"highlight%28cross%28are%29%29\"$ $\"highlight%28cross%28not%29%29\"$ is a perfect square
\n" ); document.write( "~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " Please notice how I edited your post to create an adequate meaning.\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "This sequence is an arithmetic progression with the common difference of 3 and the first term 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "When dividing by 3, all the terms of the progression give the remainder of 2.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "No one perfect square gives the remainder 2 when is dividing by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    Indeed, let's consider an arbitrary square    of an integer number \"n\".\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    If n is multiple of 3,  n = 3k,  then  is a multiple of 9; hence, it is a multiple of 3,  giving the remainder 0 whin divided by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    If n = 3k+1,  then   = , giving the remainder 1, when divided by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    If n = 3k+2,  then   = , giving the remainder 1, when divided by 3.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    It proves the statement.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );