MathDB

3

Part of 1991 National High School Mathematics League

Problems(2)

Number Theory

Source: 1991 National High School Mathematics League, Exam One, Problem 3

2/26/2020
Let aa be a positive integer, a<100a<100, and a3+23a^3+23 is a multiple of 2424. Then, the number of such aa is (A)4(B)5(C)9(D)10\text{(A)}4\qquad\text{(B)}5\qquad\text{(C)}9\qquad\text{(D)}10
number theory
Number Theory Problem

Source: 1991 National High School Mathematics League, Exam Two, Problem 3

2/26/2020
Let ana_n be the number of such numbers NN: sum of all digits of NN is nn, and each digit can only be 1,3,41,3,4. Prove that a2na_{2n} is a perfect square for all n∈Z+n\in\mathbb{Z}_+.
number theory