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Omni-MATH / Compute the sum of all positive integers a≤26 for which there exist integers b and c such that a+23b+15c−2 and 2a+5b+14c−8 are both multiples of 26.

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Compute the sum of all positive integers a≤26a \leq 26 for which there exist integers bb and cc such that a+23b+15c−2a+23 b+15 c-2 and 2a+5b+14c−82 a+5 b+14 c-8 are both multiples of 26.
Plain-text mathematical notation (without MathML)
Compute the sum of all positive integers a≤26 for which there exist integers b and c such that a+23b+15c−2 and 2a+5b+14c−8 are both multiples of 26.
Original LaTeX notation
Compute the sum of all positive integers $a \leq 26$ for which there exist integers $b$ and $c$ such that $a+23 b+15 c-2$ and $2 a+5 b+14 c-8$ are both multiples of 26.

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Source and history

task_id
625af4ee-7eeb-5594-9ec4-63b76ef35491
task_key
test--625af4ee-7eeb-5594-9ec4-63b76ef35491
task_revision_id
1
config / split
/ test

Official source

initial import