State whether True or False: If A and B are integers and A ≡ 3 (mod 3) and B ≡ 2 (mod 6) then A+B ≡ 5 (mod 6).

Show that: if a = b(mod n) and c = d(mod n), then a +c = b+d(mod n)!

20 D please

Assume all variable as positive integers. Given and O a = -2n+2 (mod 7) Which of the following is true in general? O O b = 3n+1 (mod 7) ab = 6n² +2 (mod 7) ab 6n-3 (mod 7) ab n² + 4n+ 2 ab 5n² + 4n+ 1 (mod 7) (mod 7)

In the following question: " Let a, b ∈ Z. Show that if a ≡ 5 (mod 6) and b ≡ 3 (mod 4), then 4a + 6b ≡ 6 (mod 8)." why do we ignore the -6 when substituting the variables of a and b, if we expand "4a + 6b ≡ 6 (mod 8)" we get (4a+6b)-6=8y, when we substitute we have to end up with the 8y right? Im just confused why the -6 is ignored?

please send step by step handwritten solution for Q4

Does ?2 ≡ 23 (mod 79) have any solutions. Justify your answer using the Legendre symbol.

Find all solutions to the following congruencies A.) 2x+3=7 (mod 9) B.) 2x+3=7 (mod 10)

4. Determines the result of the following operations: a. (27 – 3) (mod 5) b. (56 – 14) (mod 7) c. (6+7) (mod 2)