MathDB

P1

Part of 2019 Dürer Math Competition (First Round)

Problems(1)

Non-integers a,b,c,d

Source: 12th Dürer Math Competition , First Round ,Category E , P1

8/18/2020
Non-negative integers a,b,c,da, b, c, d satisfy the equation a+b+c+d=100a + b + c + d = 100 and there exists a non-negative integer n such that a+n=b−n=c×n=dna+ n =b- n= c \times n = \frac{d}{n} Find all 5-tuples (a,b,c,d,n)(a, b, c, d, n) satisfying all the conditions above.
number theoryalgebra