Math Is Fun Forum
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
#1 2017-11-14 07:04:18
- ATD
- Guest
A hard modular arithmetic problem
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.
#2 2017-11-24 10:44:16
- Alg Num Theory
- Member
- Registered: 2017-11-24
- Posts: 693
- Website
Re: A hard modular arithmetic problem
By direct calculation,
12! = 479001600 ≡ 736 (mod 2012),
20! = 2432902008176640000 ≡ 344 (mod 2012);
20!×12! ≡ 344×736 = 253184 ≡ 1684 (mod 2012).
Me, or the ugly man, whatever (3,3,6)
Offline
Pages: 1