Exercise 6.4 (1) For which natural numbers n is the number 3" + 1 divisible by 10? Find the remainder of the division of 1!+2!++50! by 7. (3) Is it true that 36 divides n¹ + n² +4 for infinitely many natural numbers n? Explain!

Advanced Engineering Mathematics
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Chapter2: Second-order Linear Odes
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Also its not to prove for every n, just if there exists infinitely many ns that would make the statement true
D
Exercise 6.4 (1) For which natural numbers n is the number 3" + 1 divisible by 10?
Find the remainder of the division of 1!+21+ +50! by 7.
Is it true that 36 divides n¹ + n²+ 4 for infinitely many natural numbers n? Explain!
What are the possible values of the last digit of 4", m € N
47
Transcribed Image Text:D Exercise 6.4 (1) For which natural numbers n is the number 3" + 1 divisible by 10? Find the remainder of the division of 1!+21+ +50! by 7. Is it true that 36 divides n¹ + n²+ 4 for infinitely many natural numbers n? Explain! What are the possible values of the last digit of 4", m € N 47
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