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20 Οκτ 2023 · Calculate a mod b which, for positive numbers, is the remainder of a divided by b in a division problem. The modulo operation finds the remainder, so if you were dividing a by b and there was a remainder of n, you would say a mod b = n.
\sqrt{\square} \nthroot[\msquare]{\square} \le \ge \frac{\msquare}{\msquare} \cdot \div: x^{\circ} \pi \left(\square\right)^{'} \frac{d}{dx} \frac{\partial}{\partial x} \int \int_{\msquare}^{\msquare} \lim \sum \infty \theta (f\:\circ\:g) f(x)
5 ημέρες πριν · 2^100 mod 3 = (2^50 mod 3 × 2^50 mod 3) mod 3. 2^100 mod 3 = (1 × 1) mod 3 = 1. Even faster modular exponentiation methods exist for some specific cases (if B is a power of 2). If you want to read about them and practice modular arithmetic, check out our dedicated power mod calculator.
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To find 1 mod 3 using the Modulo Method, we first divide the Dividend (1) by the Divisor (3). Second, we multiply the Whole part of the Quotient in the previous step by the Divisor (3). Then finally, we subtract the answer in the second step from the Dividend (1) to get the answer.
An odd perfect square is of the form $(2k+1)^2$. $$(2k+1)^2=4k^2+4k+1=4(k^2+k)+1$$ Since $k^2+k=k(k+1)$ is always even, $4(k^2+k)$ is always divisible by $8$. Now it follows that every odd square is congruent to $1$ modulo $8$.
All odd squares are ≡ 1 (mod 8) and thus also ≡ 1 (mod 4). If a is an odd number and m = 8, 16, or some higher power of 2, then a is a residue modulo m if and only if a ≡ 1 (mod 8). [7]
