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Given that 220≡1(mod3)and510≡1(mod3), 2^{20} \equiv 1 \pmod{3} \quad \text{and} \quad 5^{10} \equiv 1 \pmod{3}, 220≡1(mod3)and510≡1(mod3), what is the remainder when 220×510 2^{20} \times 5^{10} 220×510 is divided by 3?
What is 78×49(mod26) 78 \times 49 \pmod{26} 78×49(mod26)?
What is (6⋅6⋅6⋯6)⏟15 6’s mod 7?\underbrace{\left(6\cdot 6 \cdot 6 \cdots 6\right)}_{\text{15 6's}} \ \bmod{7}?15 6’s(6⋅6⋅6⋯6) mod7?
What is equivalent to
1!+2!+3!+⋯+100!(mod12)? 1!+2!+3!+ \cdots + 100! \pmod{12}? 1!+2!+3!+⋯+100!(mod12)?
Give your answer as an integer between 0 and 11, inclusive.
What is (10×85)(mod5)? (10 \times 85) \pmod{5} ?(10×85)(mod5)?
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