3 × 7 22 + 2 × 10 22 - 44 when divided by 18 leaves the remainder

Question

3 × 7 22 + 2 × 10 22 - 44 when divided by 18 leaves the remainder,

MARKS App · Accepted Answer

Given that: 3 × 7 22 + 2 × 10 22 - 44 = 3 × ( 6 + 1 ) 22 + 2 × ( 9 + 1 ) 22 - 44 As we know that ( 1 + x ) n = 1 + x ( C 1 n + C 2 n x + . . . . . ) = 1 + k x ; k , x ∈ I = 18 λ + 3 + 18 μ + 2 - 44 ; λ , μ ∈ I = 18 δ - 39 ; δ ∈ I = 18 β + 15 ⇒ remainder = 15

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