SSC CHSL 2020 · PYQ · Number Theory · medium
When (77⁷⁷ + 77) is divided by 78, the remainder is:
Answer
The correct answer is B: 76. 77 ≡ −1 (mod 78), so 77⁷⁷ ≡ (−1)⁷⁷ = −1 ≡ 77 (mod 78). Then 77⁷⁷+77 ≡ 77+77 = 154 ≡ 154−78 = 76 (mod 78).
- A.77
- B.76✓ Correct
- C.74
- D.75
77 ≡ −1 (mod 78), so 77⁷⁷ ≡ (−1)⁷⁷ = −1 ≡ 77 (mod 78). Then 77⁷⁷+77 ≡ 77+77 = 154 ≡ 154−78 = 76 (mod 78). The remainder is 76.
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