I'm learning about solving systems of modular linear congruences in my discrete mathematics class. Recently, my teacher posed a puzzle that I can't seem to solve:
These eight small-number triples are not random:
[[1 1 3] [1 1 4] [1 4 3] [1 4 4] [2 1 3] [2 1 4] [2 4 3] [2 4 4]]
They have something to do with the product of the first three odd
primes and the fourth power of two.
Find the connection.
From what I can tell, the triples are the cartesian products of [1 2], [1 4], and [3 4]. These add up to the first three odd primes like the teacher wanted. I still can't find a link between the triples and the fourth power of two though. My teacher said it has something to do with modular linear congruences. What am I missing?
This is an example of modular linear congruences:
$x \equiv_7 0$
$x \equiv_{11} 8$
$x \equiv_{13} 12$
Solution: $x \equiv_{1001} 987$
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