Prove that 3^105+4^105 is divisible by 13*49*181*379 but is not divisible by either 5 or 11.

 

a=3^105+4^105
OK

?a
 1645504557321331278892507061310792365037268911602846475476455267
OK
?a@13
 0
OK
?a@49
 0
OK
?a@181
 0
OK
?a@379
 0
OK
b=13*49*181*379
OK
?b
 43697563
OK
?a@b
 0
OK
?a@11
 2
OK

and of course it goes without saying, but I'll say it anyway, that a number ending in 7 is not divisible by 5.

Edited on August 16, 2011, 9:11 am

Posted by Charlie on 2011-08-16 09:10:14