Topic 2 TRUE OR FALSE Q’s
31. A
natural number is the number 0 or any number obtained by adding 1
to a natural number.
32. The
category of numbers called integers includes negative numbers.
33. A
rational number is any number that can be expressed without a
fractional part.
34. The
base of a number system determines the number of digits used in the
system.
35. The
digits used in any base are 1 through the base number.
36. ...
Prove that for every n ∈ N:
a) (10^n + 3 * 4^(n+2)) ≡ 4 mod 19, [note that 4^3 ≡ 1 mod
9]
b) 24 | (2*7^(n) + 3*5^(n) - 5),
c) 14 | (3^(4n+2) + 5^(2n+1) [Note that 3^(4n+2) + 5^(2n+1) =
9^(2n)*9 + 5^(2n)*5 ≡ (-5)^(2n) * 9 + 5^(2n) *5 ≡ 0 mod 14]