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Answer Key Basic Practice 0, 0, 5, 3, 3 What’s wrong with this computation? In the second computation, the exponent is reduced from 10 to 3 because these are equivalent modulo 7. However, only summands and factors can be reduced, i.e. you can reduce numbers that are part of a sum or part of a product. But in an exponent, such reductions aren ...
Exercise 2.3. 1. Find the least positive value of x such that (i) 71 ≡ x (mod 8) (ii) 78 + x ≡ 3 (mod 5) (iii) 89 ≡ (x + 3) (mod 4) (iv) 96 ≡ x/7(mod 5) (v) 5x ≡ 4(mod 6) 2. If x is congruent to 13 modulo 17 then 7x - 3 is congruent to which number modulo 17? 3. Solve 5x ≡ 4 (mod 6) 4. Solve 3x − 2 ≡ 0 (mod 11) 5.
Worksheet 3: Modular Arithmetic 1. Fix a positive integer m, and define the relation x ˘y by x y mod m. Prove that ˘is an equivalence relation. 2. Let a,b,c,m 2Z with m > 0. (a) Show that, if gcd(c,m) = 1, then ac bc (mod m) implies a b (mod m). (b) Give an example that shows that the gcd condition is necessary. 3.
Enjoy these free printable sheets. Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.
MODULUS FUNCTION PRACTICE . Created by T. Madas Created by T. Madas MODULUS EQUATIONS . Created by T. Madas Created by T. Madas Question 1 Solve the following equations. a) 2 1 9x+ = b) 3 6− =x c) 3 4 3 1 14x− − = ... 2 3 1x x− > + b) 4 3 2 1x x− ≤ + c) 6 2 3x x≥ ...
Get some insight on what you know about modular arithmetic via these study tools. Answer quiz questions on topics like what 'a' mod 'b' is equal to and what 10 mod 3 is. Quiz &...
The factoring polynomials worksheets require a child to take the common factor or GCF out. The expressions deal with single as well as multiple variables. Download PDF
