MathDB

1

Part of 1983 National High School Mathematics League

Problems(2)

Even Numbers

Source: 1983 National High School Mathematics League, Exam One, Problem 1

2/21/2020
p,qp,q are nonnegative integers.Given two conditions: A: p3−q3p^3-q^3 is an even number. B: p+qp+q is an even number. Then, which one of the followings are true? (A)(\text{A})A is sufficient but unnecessary condition of B. (B)(\text{B})A is necessary but insufficient condition of B. (C)(\text{C})A is sufficient and necessary condition of B. (D)(\text{D})A is insufficient and unnecessary condition of B.
Is This a Problem?

Source: 1983 National High School Mathematics League, Exam Two, Problem 1

2/21/2020
Prove that arcsin⁡x+arccos⁡x=π2\arcsin x+\arccos x=\frac{\pi}{2}, where x∈[−1,1]x\in[-1,1].