If a positive integer n, divided by 5 has a remainder 2, Which of the following must be true? I. n is odd II. n + 1 cannot be a prime number III. (n + 2) divided by 7 has remainder 2
Created: 2 years ago |
Updated: 1 year ago
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By adding 2 to all multiples of 5, you can identify the integers that have a remainder of 2 when multiplied by 5. Thus, n = 7, 12, 17, 22, etc. This series demonstrates that n does not necessarily have to be odd. Because, for instance, 12 + 1 = 13, n + 1 can also be a prime. Additionally, (n + 2)/7 occasionally yields a remainder of 2, but not always. It's important to keep in mind that the question asks us to consider what MUST be true, and we can see that none of the statements are true in every situation. However, any number of n will always result in a multiple of 5 when 3 is added
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