- #1
Chromium
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So today I was doing a problem out of my book for practice, and I came across some interesting results.
Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4.
a set of consecutive integers
1 mod 4 = 1
2 mod 4 = 2
3 mod 4 = 3
4 mod 4 = 0
5 mod 4 = 1
a set of nonconsecutive integers
6 mod 4 = 2
14 mod 4 = 2
3 mod 4 = 3
71 mod 4 = 3
35 mod 4 = 3
should the question be rephrased like this?
Show that among any group of five (not necessarily consecutive) integers, there are two or more with the same remainder when divided by 4.
Show that among any group of five (not necessarily consecutive) integers, there are two with the same remainder when divided by 4.
a set of consecutive integers
1 mod 4 = 1
2 mod 4 = 2
3 mod 4 = 3
4 mod 4 = 0
5 mod 4 = 1
a set of nonconsecutive integers
6 mod 4 = 2
14 mod 4 = 2
3 mod 4 = 3
71 mod 4 = 3
35 mod 4 = 3
should the question be rephrased like this?
Show that among any group of five (not necessarily consecutive) integers, there are two or more with the same remainder when divided by 4.