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The number 612, when divided by 13 given remainder: |
1 2 8 9 |
1 |
$6^{12}=12^6=(13-1)^6$ ${^6C}_0.13^6-{^6C}_1.13^5+{^6C}_2.13^4-{^6C}_3.13^3+{^6C}_4.13^2-{^6C}_5.13+{^6C}_6.13^0$ $=13\left[{^6C}_0.13^5-{^6C}_1.13^4+{^6C}_2.13^3-{^6C}_3.13^2+{^6C}_4.13-{^6C}_5\right]+1=1=13k+1$ when this expression is divided by 13 then remainder will be 1. |
