Cyclicity of One Digit and Two Digit Numbers, Last Two Digits of Higher Powers of Odd and Even Numbers, Shortcut for Calculating Squares of Numbers from 31 to 99

This is the 23rd video of Number System in which I have covered very important concepts of Numbers. The first thing that I have discussed in this video is the divisibility of aⁿ+bⁿ and aⁿ-bⁿ by a+b and a-b. The divisibility will vary with whether the value of n is even or odd. The different cases have been discussed in the video.

After that I have moved onto the concept of cyclicity. In this concept of cyclicity I have first showed that the cyclicity of numbers 2,3,7,8 is four and for 4 and 9 it is two and as we all know for 5 and 6 it is always one as all powers of 5 and 6 will always end with 5 and 6 respectively. Also what type of questions would be asked in this concept has been shown and the way to solve them. 

Then I have told the procedure of calculating the last two digits of higher powers of even and odd numbers. For odd numbers ending with 1, I have told a shortcut for calculating the last two digits and have shown why that is happening by solving it with the basics of Binomial Theorem. Then for odd numbers ending with 3,7 and 9, I have used the concept explained above by bringing these numbers in the form ending with 1. Here I have explained by interlinking it with one digit cyclicity as here it becomes important to have a know how of both - One Digit Cyclicity and Two Digit Cyclicity.

After this I have moved on to the method of finding out the last two digits of higher powers of even numbers. For even numbers first of all we always have to keep two things in mind - 1. (2¹⁰)^even ends always with 76 and (2¹⁰)^even always ends with 24. Using these two concepts I have extended the method two find out the last two digits of any higher power of even numbers by interlinking the even and odd term higher power properties. May be by reading it here you will find it a bit confusing but as soon as you will see the video twice or thrice the concept will become crystal clear for you. Please note that watching this video once may not suffice the purpose of understanding the concepts in detail so you may have to watch the video 2 to 3 times to understand it completely.

Also while explaining you the concept of calculating the last two digits of higher powers I have also shown how by shortcut you can calculate the squares of two digit numbers from 31 to 99 in 5 seconds if you have memorised the squares of numbers from 1 to 30. This is very important as it can tell you the last two digits of any squared number in a short time span of 5 to 10 seconds if you have done ample amount of practise.