Junior High Maths

Showing posts with label Fermat's little theorem. Show all posts

Showing posts with label Fermat's little theorem. Show all posts

Friday, 20 January 2017

Problem 20

Find the last digit of 43⁴³.

Posted by Từ Nguyên Học at 16:55 No comments:

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Labels: Chinese remainder theorem, Euler's phi function, Euler's totient function, Euler's totient theorem, Fermat–Euler theorem, Fermat's little theorem, induction, number theory, prime number, whole number

Thursday, 19 January 2017

Problem 19

Find the last digit of 2⁹⁹⁹.

Posted by Từ Nguyên Học at 15:44 No comments:

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Labels: Chinese remainder theorem, Fermat's little theorem, induction, number theory, prime number, whole number

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arithmetic (1) arithmetic sequence (2) biprime (1) calculus (1) Cartesian product (1) Chinese remainder theorem (2) composite number (1) cyclic quadrilateral (1) divisibility (6) elementary algebra (14) Euclid's formula (1) Euclidian geometry (6) Euler's phi function (1) Euler's totient function (1) Euler's totient theorem (1) exponentiation (1) Fermat–Euler theorem (1) Fermat's little theorem (2) function of one variable (1) functional equation (1) fundamental theorem of arithmetic (2) geometric sequence (1) Gregorian calendar (1) Hero's formula (1) Heron's formula (1) Heronian triangle (1) induction (9) irrational number (1) isoceles triangle (1) linear congruence equation (4) linear Diophantine equation (2) linear function (1) number theory (11) perfect square (1) polynomial factorisation (3) prime number (3) Ptolemy's theorem (1) Pythagoras' theorem (1) Pythagorean triple (4) reductio ad absurdum (4) semiprime (1) set theory (1) square root (2) summation (4) unique factorization theorem (3) unique-prime-factorization theorem (3) whole number (16)

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Problem 1

Prove that n 2 + n, where n is a whole number, is divisible by 2.
Problem 26

Prove that every composite number has a proper factor less than or equal to its square root.
Problem 28

Let ABC an isoceles triangle with AB = AC = x, BC = y. Let denote M the midpoint of AB. Find the length of CM.
Problem 27

A triangle has side lengths 1 5 , 1 3 and 4 cm. Find the length of the longest altitude.
Problem 8

Fill in the missing digit to make the number 865* divisible by 7.
Problem 18

Given a Pythagorean triple a, b, c, prove that if a is odd, then either b or c must be odd.
Problem 7

Fill in the missing digits to make the number 766776** divisible by 11.
Problem 19

Find the last digit of 2 999 .
Problem 4

The recursive formula for a sequence {u n } is written in the form: u 1 = 2 , u n+1 = 3u n , n ≥ 1 Write the general explicit ...
Problem 21

Prove that the a composite n non divisible by is a semiprime.

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▼ 2017 (31)
- ▼ January (31)
  - Problem 31
  - Problem 30
  - Problem 29
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  - Problem 27
  - Problem 26
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  - Problem 24
  - Problem 23
  - Problem 22
  - Problem 21
  - Problem 20
  - Problem 19
  - Problem 18
  - Problem 17
  - Problem 16
  - Problem 15
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