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The integer n = 12700140x3243243 is missing the digit x. a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? t for #13: Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 103 +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 = 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = 1x 1³ +2 x 1² +3 × 1¹ + 4 x 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 = 1 × 10³ +2× 10² +3 x 10¹ + 4 × 10⁰ = 1 × (-1)³ +2× (-1)² + 3x (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).

The integer n = 12700140x3243243 is missing the digit x. a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? t for #13: Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 103 +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 = 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = 1x 1³ +2 x 1² +3 × 1¹ + 4 x 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 = 1 × 10³ +2× 10² +3 x 10¹ + 4 × 10⁰ = 1 × (-1)³ +2× (-1)² + 3x (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).

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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13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
Transcribed Image Text:13) The integer n = a) If n = 3 (mod 9), then what is x ? b) If n = 3 (mod 11), then what is x ? Hint for #13: 12700140x3243243 is missing the digit x. Consider the number 1234. By writing each digit in scientific notation, we have 1234 1 x 10³ +2× 10² +3 × 10¹ + 4 × 10⁰ Then notice that 10 = 1 (mod 9). When we reduce mod 9, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x 1³ + 2 x 1² + 3 × 1¹ + 4 × 1⁰ = 1+ 2+ 3+ 4 = 10 = 1 (mod 9). Since 10 = -1 (mod 11), when we reduce mod 11, we obtain 1234 1 x 10³ +2× 10² +3 x 10¹ + 4 x 10⁰ = = 1x (-1)³ +2× (-1)² +3 × (-1)¹ +4× (-1)⁰ = -1 + 2-3 + 4 = 2 (mod 11).
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