Number Jumping: a follow-up problem to Number jumping (notes)
Number Theory
Level
pending
Bill has two numbers: 1000, and 1003. He can either add or subtract 1000, and the same thing goes for 1003. Can he reach all the numbers (including negative)?
Yes, it is possible
No, it is impossible
Impossible to tell
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1 solution
The G.C.D. (Greatest Common Divisor) of 1003 and 1000 is 1, And 1003-((1003 -1000)x334) = 1, and from there, you can either add or subtract from 1 so Yes, Bill can reach all the numbers.