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What is 4 mod 2? The mod or modulus or modulo is the remainder after dividing one number by another. Answer: 4 mod 2 is 0. Let's find 4 mod 2. Explanation: 4 mod 2 equals 0, since 4/2 = 2, with a remainder of 0. To find 4 mod 2 using the modulus method, we first find the highest possible multiple of the divisor, 2 that is equal to or less than ...
This means that a^2 = 8k + 4, where k is some integer. We can then substitute this into the equation a^2 = 4 (mod 8) to get (8k + 4) = 4 (mod 8). Simplifying this, we get 8k = 0 (mod 8), which means that a = 2 (mod 8) since 8k must be a multiple of 8 and a = 2 is the only integer that satisfies this condition. 3.
(And if you still don't believe it was fluke, then evaluate 30^1 mod 100 and mod 25 to see you don't get the same things).Assuming everything is random, there was a one in 4 chance of this happening. 2^999 is 13 mod 25, thus if we pick some thing at random that is 13 mod 25, then there is a 1 in 4 chance it was 88 mod 100.
In other words, if x^2 is a residue mod p, then x^4 is also a residue mod p. Now, let's consider the congruence x^4 ≡ 2 (mod p). Since p is congruent to 1 modulo 4, we know that p ≡ 1 (mod 4). This means that p can be expressed as p = 4k + 1 for some integer k. Substituting this into our congruence, we get x^4 ≡ 2 (mod 4k + 1).
Step 1: Divide 145 by 2. Use the integer quotient obtained in this step as the dividend for the next step. Repeat the process until the quotient becomes 0. Step 2: Write the remainder from bottom to top i.e. in the reverse chronological order. This will give the binary equivalent of 145.
Yes, it is possible. For example, if a and b are both multiples of n, then a^2 and b^2 will also be multiples of n, and thus a^2≡b^2 (mod n) will imply a≡b (mod n). 5. How can we prove that a^2≡b^2 (mod n) does not always imply a≡b (mod n)? We can prove this by providing a counterexample, as shown in question 2.
Answer: 2 mod 3 is 2. Let's find 2 mod 3. Explanation: 2 mod 3 equals 2, since 2/3 = 0 with a remainder of 2. To find 2 mod 3 using the modulus method, we first find the highest multiple of the divisor, 3 that is equal to or less than the dividend, 2. Then, we subtract that highest multiple of the divisor from the dividend to get the answer to ...
In summary: Case #1: Suppose ## n=3q+1 ## for some ## q\in\mathbb{N} ##.That is, ## n\equiv 1 \mod 3 ##.Then ## n+2\equiv 0 \mod 3 ## and ## n+4\equiv 2 \mod 3 ...
2 mod 2 = 0; 1 mod 2 = 1 - MSB (Most Significant Bit) Write the remainders from MSB to LSB. Therefore, the decimal number 8 in binary can be represented as 1000. How Many Bits Does 8 in Binary Have? We can count the number of zeros and ones to see how many bits are used to represent 8 in binary i.e. 1000. Therefore, we have used 4 bits to ...
We can divide 17 by 2 and continue the division till we get 0. Note down the remainder in each step. 17 mod 2 = 1 - LSB (Least Significant Bit) 8 mod 2 = 0; 4 mod 2 = 0; 2 mod 2 = 0; 1 mod 2 = 1 - MSB (Most Significant Bit) Write the remainders from MSB to LSB. Therefore, the decimal number 17 in binary can be represented as 10001.