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Omni-MATH / For integers a,b,c,d, let f(a,b,c,d) denote the number of ordered pairs of integers (x,y)∈{1,2,3,4,5}² such that ax+by and cx+dy are both divisible by 5. Find the sum of all possib…

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problem

For integers a,b,c,da, b, c, d, let f(a,b,c,d)f(a, b, c, d) denote the number of ordered pairs of integers (x,y)∈{1,2,3,4,5}2(x, y) \in \{1,2,3,4,5\}^{2} such that ax+bya x+b y and cx+dyc x+d y are both divisible by 5. Find the sum of all possible values of f(a,b,c,d)f(a, b, c, d).
Plain-text mathematical notation (without MathML)
For integers a,b,c,d, let f(a,b,c,d) denote the number of ordered pairs of integers (x,y)∈{1,2,3,4,5}² such that ax+by and cx+dy are both divisible by 5. Find the sum of all possible values of f(a,b,c,d).
Original LaTeX notation
For integers $a, b, c, d$, let $f(a, b, c, d)$ denote the number of ordered pairs of integers $(x, y) \in \{1,2,3,4,5\}^{2}$ such that $a x+b y$ and $c x+d y$ are both divisible by 5. Find the sum of all possible values of $f(a, b, c, d)$.

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Source and history

task_id
1afd14fd-9523-5bb6-89b1-ad3cad7d076d
task_key
test--1afd14fd-9523-5bb6-89b1-ad3cad7d076d
task_revision_id
1
config / split
/ test

Official source

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