MathDB

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Part of 2012 CHMMC Spring

Problems(2)

2012 Spring Team #1

Source:

3/20/2022
Let a,b,ca, b, c be positive integers. Suppose that (a+b)(a+c)=77(a + b)(a + c) = 77 and (a+b)(b+c)=56(a + b)(b + c) = 56. Find (a+c)(b+c)(a + c)(b + c).
number theory
2012 Spring CHMMC Tiebreaker 1 - sum x_i^2 = k for nonnegative integers

Source:

3/1/2024
Let aka_k be the number of ordered 1010-tuples (x1,x2,...,x10)(x_1, x_2, ..., x_{10}) of nonnegative integers such that x12+x22+...+x102=k.x^2_1+ x^2_2+ ... + x^2_{10} = k. Let bk=0b_k = 0 if aka_k is even and bk=1b_k = 1 if aka_k is odd. Find ∑i=12012b4i\sum^{2012}_{i=1} b_{4i}.
number theorycombinatoricsCHMMC