Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**ATD****Guest**

Could you please help me with this problem:

20! * 12! = x (mod 2012)

Some useful facts i have discovered:

1) 7 * 8 * 9 = 1 (mod 503)

2) 20! * 12! = 13 * 17 * 19 mod(503)

I have been trying to solve this problem for a long time. If you can find the answer, could you please show the step by step solution? Thank you for your help.

**Alg Num Theory****Member**- Registered: 2017-11-24
- Posts: 224
- Website

By direct calculation,

12! = 479001600 ≡ 736 (mod 2012),

20! = 2432902008176640000 ≡ 344 (mod 2012);

20!×12! ≡ 344×736 = 253184 ≡ 1684 (mod 2012).

Offline

Pages: **1**