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Form of integer

Source: Tuymaada 2015, Day 2, Problem 6, Senior League

July 10, 2017
number theoryalgebra

Problem Statement

Let 0≤b≤c≤d≤a0 \leq b \leq c \leq d \leq a and a>14a>14 are integers. Prove, that there is such natural nn that can not be represented as n=x(ax+b)+y(ay+c)+z(az+d)n=x(ax+b)+y(ay+c)+z(az+d) where x,y,zx,y,z are some integers.
K. Kohas
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