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p.278, icon at Example 6 # 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers (in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequence that is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde = a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)

p.278, icon at Example 6 # 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers (in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequence that is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde = a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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p.278, icon at Example 6 # 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers (in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequence that is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde = a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)
Transcribed Image Text:p.278, icon at Example 6 # 3. (Problem A1 from the 1989 William Lowell Putnam Mathematics Competition.) Consider the sequence of integers (in base 10): 101, 10101, 1010101, 101010101, 10101010101,.... Prove that 101 is the only number in this sequence that is prime. (Hint: Use place value to write each number in terms of the sum of its digits; for example, abcde = a10+ + b10³ + c10² + d10+ e. Then examine how the sum might be factored.)
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