Modular Arithmetic and Modulo Congruence 

I am using FinalCut Pro X in all my videos. Though the “modular arithmetic wheel/clock” is a series of gif images i built in Powerpoint :)

10 and 2 have the same remainder, which is 2, when divided by 4. 10 divided by 4 is 2 remainder 2, while 2 divided by 4 is 0 remainder 2.

3 minus 20 is -17… and add 5 multiple times, and you’ll get 3. Not 2. That is why 3 - 20 at modulo 5 is 3.

@@xanmos i dont get that part because i also got the answer as two

you may also apply the concept in determining a modular equation if it's a True congruence or not such that (a-b)/n should result in an integer by trial & error (a - (-17))/5 we can substitute a={0,1,.., n-1} = {0,1,2,3,4} when a= 3: (3 + 17)/ 5 = 4 ( wherein 4 is an integer) therefore a= 3 3=-17mod 5

3 - 20 is -17 So at modulo 5, you just have to keep on adding 5… until you get a number from 0 to 4 And that is 3.

@@xanmos pero magiging 15 po yon pag kineep up ang pag aadd then pag mininus is magiging -2 or 2 kase yon ung remainder?pa reply po thanks po medyo nalito lng po

@@gwynethfaner5741 same here. also confused with the 3-20 and his answer being -3

Remember that modulo arithmetic is the Remainder, so 208 mod 10 is 8 because 208 when divided by 10 gives us a remainder 8.

-17 is congruent to 10 mod 3 because -17 and 10 have the same remainder (1) when divided by 3 85 is congruent to -5 mod 9 because 85 and -5 have the same remainder (4) when divided by 9. 80 is not congruent to 12 mod 8, because 80 has a remainder of 0, while 12 has a remainder of 4 when divided by 8.

Ay tama pala , nakalimutan ko i subtract pa yung result sa modulo pag negative