Number Theory, Chinese Remainder Theorem

The Chinese Remainder Theorem provides a way to solve systems of simultaneous linear congruences with pairwise coprime moduli. Questions typically involve finding an integer that satisfies several such congruence relations.

• Question

  A grasshopper can jump `80` centimeters forward or `50` centimeters backward. Can the grasshopper move away from its starting point in fewer than `7` jumps to a distance of exactly one meter and `70` cm?

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  Topics:

  Arithmetic Number Theory -> Chinese Remainder Theorem Algebra -> Word Problems Proof and Example -> Constructing an Example / Counterexample Combinatorics -> Case Analysis / Checking Cases -> Processes / Procedures Algebra -> Equations -> Diophantine Equations