perplexus.info :: Just Math : Totient Trial

Totient Trial (Posted on 2016-10-24)

It is observed that Φ(1)=1 and, Φ(2)=1, where Φ(x) denotes Euler's totient function.
So for x=1, it is trivially observed that each of Φ(x) and Φ(x+1) is a perfect square.

(A) What is the next positive integer value of x such that each of Φ(x) and Φ(x+1) is a perfect square?

(B) What is the value of x with 2000 ≤ x ≤ 2100 such that each of Φ(x) and Φ(x+1) is a perfect square?

Submitted by K Sengupta

Rating: 5.0000 (1 votes)

Solution: (Hide)

x x+1 totient function values 1 2 1 1 125 126 100 36 504 505 144 400 512 513 256 324 513 514 324 256 629 630 576 144 679 680 576 256 1358 1359 576 900 1728 1729 576 1296 1970 1971 784 1296 2047 2048 1936 1024 2834 2835 1296 1296
For an explanation, refer to:
• The computer program assisted solution submitted by Charlie in this location.
• The solution submitted by Jer in this location.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
computer solution	Charlie	2016-10-24 19:16:26
My way	Jer	2016-10-24 13:39:57

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