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

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

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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
Transcribed Image Text: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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