MathDB

5

Part of 2024 Czech-Polish-Slovak Junior Match

Problems(2)

Smallest n with 4S(n)=3S(2n)

Source: Czech-Polish-Slovak Junior Match 2024, I-5

5/29/2024
For a positive integer nn, let S(n)S(n) be the sum of its decimal digits. Determine the smallest positive integer nn for which 4⋅S(n)=3⋅S(2n)4 \cdot S(n)=3 \cdot S(2n).
number theorynumber theory proposedsum of digits
A palindromic property of powers of two?

Source: Czech-Polish-Slovak Junior Match 2024, T-5

5/29/2024
Is there a positive integer nn such that when we write the decimal digits of 2n2^n in opposite order, we get another integer power of 22?
number theorynumber theory proposedDigitspalindromesPowers of 2