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    1. Welcome to the forum
    2. Daily Challenge Course Discussion
    3. M5 Number Theory Tools
    4. Week 3
    5. Day 10
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    • Module 5 Day 10 Challenge Part 1

      Satisfying Two Modular Congruencies

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    • Module 5 Day 10 Challenge Part 2

      Difference Between Solutions

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    • Module 5 Day 10 Challenge Part 3

      Table of Remainders

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    • Module 5 Day 10 Challenge Part 4

      Cycling Period of Remainders

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      audreyA

      @neatlobster Great question! Think about the grid box corresponding to a number N. The box has a purple number (N mod 5) and a yellow number (N mod 6).

      We want the yellow number to be even. Write N as 6a + b, where b is N mod 6. For instance, if N is 19, we'd let a = 3 and b = 1. But because any multiple of 6 is even, this implies that 6a is always even. And we want the yellow number, which is b, to be even. So, 6a + b = N must be even since both 6a and b are even. (Basically, the whole point of the bolded sentence is to show that N is even)

      From there, we want the purple number (N mod 5) to be even. BUT we already established that N is even! Therefore, N = 5*(even number) + (even number). (If N = 5*(odd number) + (even number), N would be odd, which can't be true)

      Hope this explanation helped! 🙂

    • Module 5 Day 10 Challenge Part 5

      Cycling Period of Remainders

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    • Module 5 Day 10 Challenge Part 6

      Cycling Period of Remainders

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    • Module 5 Day 10 Challenge Part 7

      Cycling Period of Remainders

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      西瓜西

      Okay, thanks! 🙂 @professionalbronco

    • Module 5 Day 10 Your Turn Part 1

      Non-Prime Modulus

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    • Module 5 Day 10 Your Turn Part 2

      Chinese Remainder Theorem

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    • Module 5 Day 10 Your Turn Part 3

      Chinese Remainder Theorem

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