Concept

How can you recognize impossible claims about modular remainders?

Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1

"6. If I told you that 98,243,917,215 mod 7 was equal to 1, would you call me a liar without even having to think too hard? No, you shouldn’t. It turns out that the answer is 3, not 1, but how would you know that without working hard for it?\n\n7. If I told you that 273,111,999,214 mod 6 was equal to 6, would you call me a liar without even having to think too hard? Yes, you should. Any number mod 6 will be in the range 0 through 5, never 6 or above. (Think in terms of repeatedly taking out groups of six from the big number. The mod is the number of stones you have left when there are no more whole groups of six to take. If towards the end of this process there are six stones left, that’s not a remainder, because you can get another whole group!)"

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How can you recognize impossible claims about modular remainders? | Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk | Bifalgorithm | Bifalgorithm