M2693

Part of Kvant 2022

Problems(1)

Sum of digits of factorial

Source: Kvant Magazine No. 3 2022 M2693

Prove that there exists a natural number

b

such that for any natural

n>b

the sum of the digits of

n!

is not less than

10^{100}

.
Proposed by D. Khramtsov

Kvantnumber theory