1

Part of 1963 German National Olympiad

Problems(1)

dividing a prime number by 30 or 60

Source: 1962-63 Germany R4 12.1

a) Prove that when you divide any prime number by

30

, the remainder is either

1

or is a prime number! b) Does this also apply when dividing a prime number by

60

? Justify your answer!

number theoryremainderDivide