Modular Arithmetic Number Theory 8 Youtube Suggest a problem: forms.gle ea7pw7hckepgb4my5please subscribe: michaelpennmath?sub confirmation=1patreon: patreo. ⭐support the channel⭐patreon: patreon michaelpennmathmerch: teespring stores michael penn mathmy amazon shop: amazon .
Modular Arithmetic Number Theory 8 Youtube Sign up with brilliant and get 20% off your annual subscription: brilliant.org majorprep stemerch store: stemerch support the channel: ht. We can solve this problem using mods. this can also be stated as . after that, we see that 7 is congruent to 1 in mod 4, so we can use this fact to replace the 7s with 1s, because 7 has a pattern of repetitive period 4 for the units digit. is simply 1, so therefore , which really is the last digit. Explore the fundamental concepts of modular arithmetic in this 26 minute video lecture on number theory. delve into the eighth installment of a comprehensive series, focusing on the principles and applications of modular arithmetic within the broader context of number theory. Here, dividend = a. divisor = b. quotient = q, and. remainder = r. in modular arithmetic, it is written as a mod b = r, read as ‘a modulo b equals r’ where ‘b’ is referred to as modulus. this means if we divide ‘a’ by ‘b’ the remainder is ‘r.’. for example, 14 3 = 4, r e m a i n d e r 2 ⇒ 14 mod 3 = 2, which means if 14 is.
Number Theory Modular Arithmetic Introduction Lecture 8 Explore the fundamental concepts of modular arithmetic in this 26 minute video lecture on number theory. delve into the eighth installment of a comprehensive series, focusing on the principles and applications of modular arithmetic within the broader context of number theory. Here, dividend = a. divisor = b. quotient = q, and. remainder = r. in modular arithmetic, it is written as a mod b = r, read as ‘a modulo b equals r’ where ‘b’ is referred to as modulus. this means if we divide ‘a’ by ‘b’ the remainder is ‘r.’. for example, 14 3 = 4, r e m a i n d e r 2 ⇒ 14 mod 3 = 2, which means if 14 is. By the way, this also give us an algorithm to find all solutions to a modular equation k x ≡ l mod n. use extended euclidean algorithm to solve k x − n y = l for some values of x, y. take x ≡ t mod n such that 0 ≤ t <n. save the gcd (k, n) = d. find all other solutions t i d for all values 0 ≤ i <d. Example #4. for this problem, suppose we wanted to evaluate 97 mod 11. well, 97 divided by 11 equals 8 remainder 9. but since this remainder is negative, we have to increase our quotient by 1 to say 97 divided by 11 equals 9 remainder 2, as 11 ( 9) 2 = 97! therefore, 97 mod 11 equals 2!.
Modular Arithmetic Number Theory Youtube By the way, this also give us an algorithm to find all solutions to a modular equation k x ≡ l mod n. use extended euclidean algorithm to solve k x − n y = l for some values of x, y. take x ≡ t mod n such that 0 ≤ t <n. save the gcd (k, n) = d. find all other solutions t i d for all values 0 ≤ i <d. Example #4. for this problem, suppose we wanted to evaluate 97 mod 11. well, 97 divided by 11 equals 8 remainder 9. but since this remainder is negative, we have to increase our quotient by 1 to say 97 divided by 11 equals 9 remainder 2, as 11 ( 9) 2 = 97! therefore, 97 mod 11 equals 2!.
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