Let a and b be non relatively prime positive integers. If there exist integers s and t with as+bt=2 then' O gcd(a,b)=2 a and b are relatively prime O gcd(a,b)=4 O gcd(a,b)=3 None of these

integer of the form okts is also but not' conversely

I need the answer as soon as possible

(9) Prove that for integers x, y and z, if x² + y² = z² then either æ or y is even.

Prove that there exists an n ∈ N such that 7 | (3^n − 1).

How do I prove the following statements: (a) For all a, b, c ∈ Z, if a < b, then a + c < b + c.(b) For all integers a, b, if 0 < a and a < b, then a^2<b^2(c) 0 < 1 Using these rules: ● (O1) If a ∈ Z, then exactly one of the following is true: 0 < a, a = 0, 0 > a. ● (O2) For all a, b ∈ Z, if 0 < a and 0 < b, then 0 < a + b. ● (O3) For all a, b ∈ Z, if 0 < a and 0 < b, then 0 < a ⋅ b. ● (O4) for all a, b ∈ Z, a < b exactly when 0 < b − a.

Give a combinatorial proof for the identity 1+2+3+..+n= (",").

Prove that 1 8000 +28000 38000 +4 8000 + 5 + 8000 8000 Theorem (and not a calculator). + 6 is a multiple of 13 using Fermat's Little