Given that 5^j+6^k+7^d+11^m=2006 where j, k, d and m are different non-negative integers, what is the value of j+k+d+m?

Since the sum of 3 odds and an even is odd, k=0. --> 5^j + 7^d + 11^m = 2005. Now 7^4 >2005 so d<4. Also 7^d + 11^m =0 mod 5 --> 2^d=4 mod 5 --> d=2 --> 5^j + 11^m =1956 --> 5^j=9 mod 11 --> j=4 mod 11 but 5^5>1956 so j<5 --> j=4 --> 11^m=1331 --> m=3.

So j+k+d+m=9

Posted by Dennis on 2007-02-26 10:49:50