Bifalgorithm post · Brisk · Chapter 1

How can you recognize impossible claims about modular remainders?

How can you recognize impossible claims about modular remainders? (Brisk · Chapter 1) — "6. If I told you that 98,243,917,215 mod 7 was equal to 1, would you c…

Ideas in this flowchart

Using remainder bounds to judge claims about large-number modulo calculations
The claim that 98,243,917,215 mod 7 equals 1 should not be rejected without calculation.
The actual remainder is 3, so the claim is false.
Determining this remainder requires carrying out the calculation.
The claim that 273,111,999,214 mod 6 equals 6 should be rejected immediately.
Any number modulo 6 must have a remainder from 0 through 5.
A remainder is what remains after removing all possible complete groups of six.
If six stones remain, they form another complete group, so six is not a remainder.

Bifalgorithm

Feed/

How can you recognize impossible claims about modular remainders?

Channel

Brisk

1 page

USR292600b83e2a

Ebook3w

"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!)"

Flowchart preview

👍

0 comments0 shares