MATHmaniac aka CrUNchy

Definition:
An arithmetic function is a function that defined for all positive integers

Definition:
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.

Let's see...
and are multiplicative function.
Let say . Find and .


Positive divisor of n=

by multiplying P,



thus,


Get it??
Let's use number,..






thus,
Let say k=5,so

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source from internet

THE FIRST CONTACT BETWEEN
MATHEMATIC AND AL-QUR'AN

Translated by Abdullah Yusuf Ali.
"He is the First and the Last, the Evident and the Immanent: and He has full knowledge of all things".

This is a commentary of Maulana Muhammad Ali from his book:
"The Holy Quran Arabic Text with English Translation, Commentary and comprehensive Introduction"
About surah 57 verse 3

The Holy Prophet has thus explained the four attributes of the Divine Being
mentioned here:

“Thou art the First, so that there was nothing before Thee, and Thou art
the Last, so that there is nothing after Thee, and Thou art the Manifest, or the Ascendant
over all, so that there is nothing above Thee, and Thou art the Hidden, the Knower of the
hidden things, so that there is nothing hidden from Thee” (Muslim. 48:13).

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REDUCTION MOD P

maple can do computations with integers modulo m.
By using maple:

> modp(117,13);
0
> modp(129,13);
12
> ifactor(129-12);
(3)2 (13)
> 117 mod 13;
0
> 129 mod 13;
12
> 1/17 mod 257;
121
> modp(121*17,257);
1

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),

and this is indeed the case in as much as 13 divides the difference 129−12. The
call 129 mod 13 also reduced 129 modulo 13. When a and m are relatively prime,
i.e., 1 is their greatest common divisor, modp(1/a,m) or 1/a mod m returns the
multiplicative inverse of a modulo m. We see that 121 is the inverse of 17 modulo
257, and indeed

(121)(17) ≡ 1 (mod 257).

U can try it by u'rself!!!

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FAMILIAR WITH MAPLE SOFTWARE?


For those who's taking KOS 1110....(computer in Science).....
U can try This exercise......

Gcd and lcm
The greatest common divisor and the lowest common multiple of a set of
numbers can be found using gcd and lcm.

> gcd(28743,552805);
11
> ifactor(28743); ifactor(552805);
(3) (11) (13) (67)
(5) (11) (19) (23)2


> lcm(21,35,99);
3465

We find that the gcd of 28743 and 552805 is 11. This can also be seen from the
prime factorizations.
The lcm of 21, 35, and 99 is 3465.

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