O T O(2016)(a). What is the highest power of 15 that divides1000Be 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 +2"+2 for all n20.( 3999(d). Find the smallest positive residue r such thatEr (mod 26).(e). For which integers c, 0 1, we define K, = 2²" + 5. In the sequence K,,K2,K3,.….. can there be a primenumber? Justify.FiltersAdd a caption.> My group

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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

Chapter10: Sequences, Series, And Probability

Section: Chapter Questions

Problem 59RE

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Question

O T O
(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 +2"+2 for all n20.
( 3999
(d). Find the smallest positive residue r such that
Er (mod 26).
(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 K,,K2,K3,.….. can there be a prime
number? Justify.
Filters
Add a caption.
> My group

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