2.2: Order and factors
Problem 44 Find the remainder when we divide
1111 · · · 1111 (with 1111 digits 1)
by 1111.
Problem 45 Which of the numbers
is bigger?
Problem 46 Show that the integer
100 000 000 003 000 000 000 000 700 000 000 021
is not prime.
Problem 47 How many prime numbers are there in each of these sequences? (Can you identify infinitely many primes in either sequence? Can you identify infinitely many non-primes?)
(a) 1, 11, 111, 1111, 11111, 111111, 1111111, ...
(b) 11, 1001, 100001, 10000001, ...