4

Part of 1998 Czech And Slovak Olympiad IIIA

Problems(1)

greatest power of 3 that divides day^{month} −1998

Source: Czech And Slovak Mathematical Olympiad, Round III, Category A 1998 p4

For each date of year

1998

, we calculate day

^{month}

−year and determine the greatest power of

3

that divides it. For example, for April

21

21^4 - 1998 =192483 = 3^3 \cdot 7129

, which is divisible by

3^3

3^4

. Find all dates for which this power of

3

is the greatest.

number theorymaxpower of 3