MathDB

2

Part of 2023 May Olympiad

Problems(2)

min, max (a+c+e) if a+b+c+d+e=1002 pos. integers

Source: 2023 May Olympiad L2 p2

3/24/2024
Let a,b,c,da, b, c, d, and ee be positive integers such that a≤b≤c≤d≤ea\le b\le c\le d\le e and that a+b+c+d+e=1002a+b+c+d+e=1002. a) Determine the largest possible value of a+c+ea+c+e. b) Determine the lowest possible value of a+c+ea+c+e.
number theory
a^4+b^3+c^2+d =\overline{cd} (2023 May Olympiad L1 p2)

Source:

3/24/2024
We say that a four-digit number abcd‾\overline{abcd} is slippery if the number a4+b3+c2+da^4+b^3+c^2+d is equal to the two-digit number cd‾\overline{cd}. For example, 20232023 slippery, since 24+03+22+3=232^4 + 0^3 + 2 ^2 + 3 = 23. How many slippery numbers are there?
number theory