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Algebra Level 2

Find the remainder when 16 ! − 15 16! -15 is divided by 14 ! − 2 14! - 2 .

485 430 437 465

Pankaj Joshi by Pankaj Joshi , 23, India

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1 solution

( 14 ! − 2 ) × 15 × 16 = 14 ! × 15 × 16 − 2 × 15 × 16 = 16 ! − 480 (14! - 2) \times 15 \times 16 = 14! \times 15 \times 16 - 2 \times 15 \times 16 = 16! - 480

⇒ 16 ! − 480 ≡ 0 ( m o d 14 ! − 2 ) \Rightarrow 16! - 480 \equiv 0 \pmod{14! - 2}

16 ! ≡ 480 ( m o d 14 ! − 2 ) 16! \equiv 480 \pmod{14! - 2}

16 ! − 15 ≡ 465 ( m o d 14 ! − 2 ) 16! - 15 \equiv 465 \pmod{14!-2}

Therefore, remainder when 16 ! − 15 16! - 15 is divided by 14 ! − 2 14! - 2 is 465 \boxed{465}

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What is this mod?

Ashutosh Srivastava - 7 years, 1 month ago

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