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You can put this solution on YOUR website!
You can figure this out a couple of ways, but I will show you how I would do it using modular arithmetic and congruences. \r
\n" ); document.write( "\n" ); document.write( "First, 7^2=49 which is congruent to (-1) modulo 10.
\n" ); document.write( "Second, 7^1992=(7^2)^996 which is congruent to (-1)^996 modulo 10.
\n" ); document.write( "Finally, (-1)^996=1. We conclude that the unit digit of 7^1992 is 1.\r
\n" ); document.write( "\n" ); document.write( "Without going through an entire explanation and lesson in modular congruences, I will explain this as follows:\r
\n" ); document.write( "\n" ); document.write( "Consider:
\n" ); document.write( "abcdefx where a,b,c,d,e,f,x are natural numbers that form the number abcdefx (we are not talking about multiplication here). Note that this is the same as abcdef0+x. Now, 10 divides a multiple of 10. So 10|(abcdef0). We are left with x mod 10 (as 10|abcdef0 implies abcdef0 is congruent to 0 mod 10). So when we take mod 10 of any number we can think of that as asking what the last digit will be.\r
\n" ); document.write( "\n" ); document.write( "Hope this helps. \n" ); document.write( "