1) Firstly, let's check out the prime factorization of 171! We observe that the sum of digits add up to 1+7+1=9. Hence, 9 is a factor of 171. From there, we can deduce that 171=3x3x19.

We haven't got many submissions for Carnival #171. One of them is from Mr Zor Shekhtman:

2)

By now UNIZOR.COM has about 1000 lectures. The course "Math 4 Teens" is finished (though, a few exams might be added). I am working now on the new course "Physics 4 Teens". Completed the "Mechanics" part and working now on "Energy". There about 1500 followers to my YouTube channel.

Do check out the above website if you are interested in videos and courses on Maths and Physics.

3)

A great part of mathematics is psychological, to be specific, resilience is very important. Never giving up is the key to success. The AMS and MAA have recently published (and made available online) a collection of essays entitled “Living Proof: Stories of Resilience Along the Mathematical Journey”. Each author contributes a story of how they encountered some internal or external difficulty in advancing their mathematical career, and how they were able to deal with such difficulties. More details are available on Professor Terence Tao's website: https://terrytao.wordpress.com/2019/06/27/living-proof-stories-of-resilience-along-the-mathematical-journey/

Do check it out if you need some additional motivation in your mathematical journey.

4)

I would like to recommend Joseph Nebus' blog: https://nebusresearch.wordpress.com/. If you haven't already done so, do check it out! It is full of interesting mathematical tidbits like comics, and expository essays targeting the general audience, for example his "A to Z" series of essays.

5)

Do check out my other carnival post on "Playful Math Education"! It can be accessed at: https://mathtuition88.blogspot.com/2019/02/playful-math-education-carnival-125.html.

6)

For an alternative proof that the square root of 2 is irrational, check out this post. It can be said to be a more "constructive" approach than the popular proof by contradiction, though some may argue that it is not the case.

7)

For more advanced readers, you may want to check out this post on Fermat's Two Squares Theorem. It explains why certain numbers can be expressed as the sum of two squares, for instance 13=2^2+3^2.

8)

Lastly, let's end off with a Math video, with the highly popular and recommended channel 3Blue1Brown. It is on the very hot topic of Neural Networks: