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MATHmaniac aka CrUNchy: The Theory Of Congruences
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CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. The Theory Of Congruences. Let n be a fixed point positive integer. Two integers a and b are said to be congruent modulo n if na-b,symbolized by;. A ≡ b (mod n). Any number divide by 6, the remainder will either be 0,1,2,3,4,5, or 6. We divided into 6 classes when measure by 6:. Class 1 = {…,-18,-12,-6, 0. 6,12,18,…}. Class 2 = {…,-17,-11,-5, 1,. 7,13,19,…}. Class 3 = {…,-16,-10,-4, 2.
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MATHmaniac aka CrUNchy: January 2009
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CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. 1) When Mr. Smith cached a check at his bank, the teller mistook the number of cents for the number of dollars and vice versa. Unaware of this, Mr. Smith spent 68 cents and then noticed to his surprise that he had twice the amount of the original check. Determine the smallest value for which the check could have been written. Hint: 7x 11y = 100). This is my fav:. Subscribe to: Posts (Atom).
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MATHmaniac aka CrUNchy: Using Maple
http://mathmaniac-crunchy.blogspot.com/2009/04/dont-u-know-that.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. FAMILIAR WITH MAPLE SOFTWARE? For those who's taking KOS 1110.(computer in Science). U can try This exercise. The greatest common divisor and the lowest common multiple of a set of. Numbers can be found using gcd and lcm. Ifactor(28743); ifactor(552805);. 3) (11) (13) (67). 5) (11) (19) (23)2. Lcm(21,35,99);. We find that the gcd of 28743 and 552805 is 11. This can also be seen from the.
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MATHmaniac aka CrUNchy: Pell's Equation
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CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. Give 3 positive solutions. Find the continued expansion of. Since n=2 and it is even, the solutions are. Where k=1,2,3. Are the positive solutions. Calculate the value of the numerator and denominator,. So,the answers for 3 positive solutions of. Subscribe to: Post Comments (Atom). View my complete profile. Ada Apa Dengan Math (AADM). Some said I hate math. Some said I love math.
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MATHmaniac aka CrUNchy: April 2009
http://mathmaniac-crunchy.blogspot.com/2009_04_01_archive.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. 1)Find the continued fraction of. Find the gcd(13,7). 2)Find the continued fraction of. 2nd step: find the gcd (23,21). 23=1 x 21 2. 21=10 x 2 1. Prove that for any integer a, 3 a 3-a. Let a be an integer.when we divide by 3,. We have 3 possiblities:. We want to show that 3 divides a 3-a. We know that a 3=a(a 2-1)=a(a-1)(a 1). If a=3k,then a 3=3.k(3k-1)(3k 1). Thus,3 a 3-a for a=3k. Now,Us...
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MATHmaniac aka CrUNchy: Fermat's Theorem
http://mathmaniac-crunchy.blogspot.com/2009/04/fermats-theorem.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. Let P be a prime number and suppose that P is not divisible by a.Then,. If P is a prime number,then. For any integer a. Now,Using Fermat's Theorem we're going to proof:. Theorem 1 said,. How (P-1) become congruence to -1? Ok,let's say P as 19. So,when (19-1) become 18,then. THEOREM 2 said,. Again P as 19,thus. Subscribe to: Post Comments (Atom). View my complete profile. We Think Math Best.
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MATHmaniac aka CrUNchy: MAPLE Again
http://mathmaniac-crunchy.blogspot.com/2009/04/maple-again.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. Maple can do computations with integers modulo m. 117 mod 13;. 129 mod 13;. 1/17 mod 257;. The functions for reduction modulo m are modp and mod. Given an integer a and. A positive integer m, modp(a,m) reduces a modulo m. The syntax using mod is. A mod m. In our maple session, modp(129,13) returned 12, which means. 129 ≡ 12 (mod 13),. 257, and indeed. 121)(17) ≡ 1 (mod 257).
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MATHmaniac aka CrUNchy: THANK YOU,SIR
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CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. To all our lecturers,Dr Jesni,Prof Torla and of course,Br Supian. Thank you so much for teaching us this whole sem,. We also want to apologize for any mistakes that we have done,. You guys are not only our lecturers but also a brother and father to us. Same to all friends,. Sorry,Thank You and Good Luck in everything! Subscribe to: Post Comments (Atom). View my complete profile.
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MATHmaniac aka CrUNchy: Number Theoretic Function-Part 2
http://mathmaniac-crunchy.blogspot.com/2009/04/number-theoretic-function-part-2.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. Number Theoretic Function-Part 2. An arithmetic function is a function that defined for all positive integers. An arithmetic function f is called multiplicative if f(mn) = f(m) f(n) whenever m and n are relatively prime positive integers.It is called multilplicative if. F(mn) = f(m) f(n) for all positive integers m and n. Positive divisor of n=. By multiplying P,. Let's use number,.
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MATHmaniac aka CrUNchy: Extra information!!!
http://mathmaniac-crunchy.blogspot.com/2009/03/extra-information.html
CLICK HERE FOR BLOGGER TEMPLATES. Mathematics is the Queen of Science and Number Theory is the Queen of Mathematics. The most generally enduring problem of number theory is probably that of diophantine equations. Greek mathematicians were quite adept at solving in integers x and y the equation. 1) f(x,y) = ax2 bzy cy2 dx ey f = o,. A prime number p is representable in an essentially unique manner by the form x2 y2 for integral x and y if and only if p = 1 modula 4 (orp = 2). It is easily verified that.
