Question

Aratati ca nr :a=6^1996+5^1997-4^1998 si b=1×2×3×......×1997+5 sunt divizibile cu 5.

Answer 1

a = 6^1996 + 5^1997 - 4^1998

u(4^1998) = u[(4^2)^999] =u(16 ^999) = 6

u( 6^1996 + 5^1997 - 4^1998) =u(6 + 5 - 6) = 5 ⇒ a ⋮ 5

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b = 1•2•3• 4 •5• ... •1997 + 5

1•2•3• 4 •5• ... •1997 ∈ M₅ ⇒ 1•2•3• 4 •5• ... •1997 + 5 ∈ M₅ ⇒ b ⋮ 5