DT6248 Discrete Maths Modular Arithmetic
Homework
1) The following statements are false. Provide counterexamples.
a) If a  b n 0, then a n 0 or b n 0.
b) If a 3  n 0 then a 2  n 0.
2) Find solutions for x in each if the following equations.
a) 2 x  3 15 7
b) x 2  x 11 1
c) 3x  4mod8
d) 8x  7 mod18
3) Prove the following: For any integer n  0 and for all integers a, b, c, and b , if
a n b and c n d then ac n bd .
4) Prove that 3n  6 3 .
5) What is the last digit of 43214321?
6) What is the last digit of 3400.
7) Prove that 7 42  22  1
n
n
8) Prove that the equation x 2  3 y  5 has no solutions in integer numbers.
9) Prove that the equation 3x 2  4 y  5 has no solutions in integer numbers.
10) Prove that 10 divides 1110  1 .
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