MathDB

5

Part of 2024 Assara - South Russian Girl's MO

Problems(2)

2024^8 | 2024!

Source: Assara 2024 J5

10/14/2024
Prove that 2024!2024! is divisible by a) 202422024^2; b) 202482024^8. (n!=1⋅2⋅3⋅...⋅nn!=1\cdot 2 \cdot 3 \cdot ... \cdot n) Z.Smysl
number theory
(100!)^99 > (99!)^100 > (100!)^98 .

Source: Assara 2024 S5

10/14/2024
Prove that (100!)99>(99!)100>(100!)98(100!)^{99} > (99!)^{100} > (100!)^{98}. K.A.Sukhov
algebrainequalities