Question

Answer the following questions using modular arithmetic
a) Determine if 5201,001 −2 is divisible by 3.
b) Determine all of the zeros of the polynomial p(x) = x2 + x mod6.
c) Show that if a2 + b2 = c2, then a ≡ 0,2 mod 4 or b ≡ 0,2 mod 4

Answer 1

PAGE NO: DATE Amo a, 5201,001-2 - 5200999 5200499- 1733666:33 . 5201,001 & 2 (mod 3) 6 px) = x² + x mod 6 ginen polynomial + x²+x as x + x = 0 mod 6 ) x(x+1)=0 (modo) as 6=2.3 ×(x+1)=0 (mod 2) x(+1) = 0 (mod 3) xel__ .: the zeros of the polynomial are x=0, x=-1,x=1,x=2 Un E2, n2 = 0, 1 (mod 4) =) a² + b ² (² 0,1 (mod4). then azo, a mod u b= 0, 2 mod 4

PAGE NO.: DATE: a² = 1 oro (mod 4) 6² = 1 oro (modu) C. 1ero (modu) Adding two squares is not a (mod 4) . i cz1 (mod4) 4% or 416 cho (mod4) . 41a or 416 well, this to the most elementary solution of this Honce Proud brohlam o