- #1
triac
- 20
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Homework Statement
Okay, so I'm going to find the smallest positive remainder of (21999+31998+51997) divided by seven.
Homework Equations
The Attempt at a Solution
Well, I did like this:
23 is congruent to 1 (mod 7). Therefore, 21999= (23)1999/3 is congruent to 1 (mod 7).
33 is congruent to (-1) (mod 7). Therefore, 31998=(33)666 is congruent to (-1)666=1 (mod 7).
53 is congruent to (-1) (mod 7). Therefore, 51997=(53)665*25 is congruent to (-1)665*4 = -4 (mod 7)
So, all in all the remainder should be two. However it says in the key that it is six, and I can't see where I'm wrong. Got any suggestions?