Chapter 3, Problem 14

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Prove or disprove

(x mod ny) mod y = x mod y, for all integer n

• Problem Solution

Thus we get

q= (m‐nt)y + p

(m‐nt) is an integer, and |p|

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Prove or disprove (x mod ny) mod y = x mod y, for all integer n • Problem Solution Thus we get q= (m‐nt)y + p (m‐nt) is an integer, and |p|

Prove or disprove (x mod ny) mod y = x mod y, for all integer n • Problem Solution According to our assumptions, we have proved 1) (x mod ny) mod y = p 2) x mod y = p Hence we proved (x mod ny) mod y = x mod y ,for all integer n 2008‐4‐17 9

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Chapter 3, Problem 14

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