Aspire Faculty ID #16456 · Topic: NIMCET 2009 · Just now
NIMCET 2009

Find the unit digit of $(13647)^{3265}$.

Solution

Unit digit depends on unit digit of base: 7. 
Powers of 7 cycle every 4: 
$7^1 = 7$ 
$7^2 = 49$ → 9 
$7^3 = 343$ → 3 
$7^4 = 2401$ → 1 
Cycle: 7, 9, 3, 1 
 Find exponent mod 4: $3265 \bmod 4 = 1$ 
 So unit digit = 7.

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