nasex3 - NUMBERS AND SETS EXAMPLES SHEET 3. W. T. G. 1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: NUMBERS AND SETS EXAMPLES SHEET 3. W. T. G. 1. Solve (ie., find all solutions of) the equations (i) 7 x 77 (mod 40). (ii) 12 y 30 (mod 54). (iii) 3 z 2 (mod 17) and 4 z 3 (mod 19). 2. Without using a calculator, work out the value of 17 10 , 000 (mod 31). 3. Again without using a calculator, explain why 23 cannot divide 10 881- 1. 4. Let a 1 = 6 and for n > 1 let a n = 6 a n- 1 . What is a 2002 (mod 91)? 5. An RSA encryption scheme ( n,d ) has modulus n = 187 and coding exponent d = 7. Factorize n , and hence find a suitable decoding exponent e . If you have a calculator, check your answer by encoding the number 35 and then decoding the result. 6. Let p be a prime number and let 1 6 k < p . Prove that ( p k ) is a multiple of p . If you use any results from the course, make clear what they are and how you are using them. 7. Let P be a polynomial of the form P ( x ) = x d + a d- 1 x d- 1 + ... + a 1 x + a , where the coefficients a i are all integers. Suppose that r and s...
View Full Document

Page1 / 2

nasex3 - NUMBERS AND SETS EXAMPLES SHEET 3. W. T. G. 1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online