Congruences Worksheet

You may want to read about Congruences before doing this worksheet.

1. Find the least residue of 1215 (mod 4), (mod 10), and (mod 100).
2. Find the least residue of 1867 (mod 4), (mod 10), and (mod 100).
3. If k ≡ 1 (mod 4), then what is 6k + 5 congruent to (mod 4)?
4. To what values (mod 30) can prime numbers greater than 5 be congruent? (Hint: 30 = 2 × 3 × 5).
   Last updated December 17, 2013.

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