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# Number Theory

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What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?

Dec 11, 2021

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What is the largest number k less than 1000 such that the remainder is 1 when k is divided by each of 3, 4, and 5?

Hello Guest!

$$15\times 3\cdot 4\cdot 5=900\\ 16\times 3\cdot 4\cdot 5=960\\ 17\times 3\cdot 4\cdot 5=1020\\ k=16\times 3\cdot 4\cdot 5+1$$

$$k=961$$

!

Dec 11, 2021