2016(a). What is the highest power of 15 that divides1000).Be careful! 15 is NOT prime.(b). Given that k =3 (mod 4), determine the least nonnegative residue of 9k333 +22 (mod 4).(c). Using properties of congruences show that 7 divides 32n+1+2n+2 for all n >0.3999 – 1(d). Find the smallest positive residue r such that=r (mod 26).2(e). For which integers c, 0 1, we define K, = 22" +5. In the sequence K1,K2,K3,... can there be a primenumber? Justify.

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2016 What is the highest power of 15 that divides | 1000 Be careful! 15 is NOT prime.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.2: Properties Of Division

Problem 51E

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Question

2016
(a). What is the highest power of 15 that divides
1000).
Be careful! 15 is NOT prime.
(b). Given that k =3 (mod 4), determine the least nonnegative residue of 9k333 +22 (mod 4).
(c). Using properties of congruences show that 7 divides 32n+1+2n+2 for all n >0.
3999 – 1
(d). Find the smallest positive residue r such that
=r (mod 26).
2
(e). For which integers c, 0<c < 30, does the congruence 12x = c (mod 30) have solutions?
When the solutions exists, then how many incongruent solutions are there?
(f). Let n > 1, we define K, = 22" +5. In the sequence K1,K2,K3,... can there be a prime
number? Justify.

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