4

Part of 2024 Romanian Master of Mathematics

Problems(1)

Innovative or not so much NT with powers and remainders

Source: RMM 2024 Problem 4

a

b

1

. For any positive integer

n

r_n

be the (non-negative) remainder that

b^n

leaves upon division by

a^n

. Assume there exists a positive integer

N

r_n < \frac{2^n}{n}

for all integers

n\geq N

a

b

.
Pouria Mahmoudkhan Shirazi, Iran

RMMnumber theoryremaindersize