document.write( "Question 32297: What is the largest number of distinct postive intgers that can be found such that no four of them cab be selectedd with a sum divisable by 4? \n" ); document.write( "
Algebra.Com's Answer #18930 by venugopalramana(3286)\"\" \"About 
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WHEN A NUMBER IS DIVIDE BY 4 , WE CAN GET A REMAINDER OF 0..OR..1...OR...2..OR...3...
\n" ); document.write( "WE HAVE TO NAME INTGERS NO 4 OF WHICH WILL ADD UP TO A MULTIPLE OF 4.
\n" ); document.write( "SO LET US TAKE THE NUMBERS STARTING WITH THOSE GIVING A REMAINDER OF 0.
\n" ); document.write( "0...REMAINDER...WE CAN TAKE 3 SUCH NUMBERS..
\n" ); document.write( "1....REMAINDER....WE CAN TAKE THREE WITH THE ABOVE..AS ANY 4 TOGETHER WILL GIVE REMAINDER OF 3.OR..1..OR..2.
\n" ); document.write( "2....REMAINDER.......WE CAN NOT HAVE EVEN ONE WITH THE ABOVE...AS A SUM OF 0 REMAINDER CAN BE GOT FROM 4 OUT OF 3*0'S,3*1'S,1*2...BY TAKING...1*2+2*1+1*0
\n" ); document.write( "=4-4=0
\n" ); document.write( "3....REMAINDER .....WE CAN NOT HAVE EVEN ONE WITH THE ABOVE...AS A SUM OF 0 REMAINDER CAN BE GOT FROM 4 OUT OF 1*3,3*1,3*0...BY TAKING...1*3+1*1+2*0
\n" ); document.write( "=4-4=0
\n" ); document.write( "HENCE WE CAN HAVE A MAXIMUM OF 6 INTEGERS SAY
\n" ); document.write( "3 WITH REMAINDER 0 .....0,4,8,...
\n" ); document.write( "3 WITH REMAINDER OF 1....1,5,9.....
\n" ); document.write( "WE CAN CHECK THAT NO 4 OF THEM ADD UP TO A MULTIPLE OF 4...EX......
\n" ); document.write( "0+1+4+5=10
\n" ); document.write( "0+1+4+8=13
\n" ); document.write( "0+1+4+9=14
\n" ); document.write( "0+1+5+8=14
\n" ); document.write( "0+1+5+9=15
\n" ); document.write( "1+4+5+8=17
\n" ); document.write( "ETC...
\n" ); document.write( "...IF WE TRY TO ADD ANY NUMBER THEN WE CANT FULFILL THE REQUIREMENT ASKED. \n" ); document.write( "
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