MathDB

2

Part of 1994 National High School Mathematics League

Problems(2)

Two Statements

Source: 1994 National High School Mathematics League, Exam One, Problem 2

2/28/2020
Give two statements: (1) a,b,ca,b,c are complex numbers, if a2+b2>c2a^2+b^2>c^2, then a2+b2−c2>0a^2+b^2-c^2>0. (2) a,b,ca,b,c are complex numbers, if a2+b2−c2>0a^2+b^2-c^2>0, then a2+b2>c2a^2+b^2>c^2. Then, which is true? (A)\text{(A)} (1) is correct, (2) is correct as well (B)\text{(B)} (1) is correct, (2) is incorrect (C)\text{(C)} (1) is incorrect, (2) is incorrect as well (D)\text{(D)} (1) is incorrect, (2) is correct
complex numbers
The 1000th Number

Source: 1994 National High School Mathematics League, Exam Two, Problem 2

3/2/2020
Find the 1000th number (from small to large) that is coprime to 105105.