The theory of numbers, by Robert D. Carmichael ...

CONTENTS
CHAPTER I. ELEMENTARY PROPERTIES OF INTEGERS
PAGE
~ I. FUNDAMENTAL NOTIONS AND LAWS................................ 7
~ 2. DEFINITION OF DIVISIBILI. THE UNIT........................... 8
~ 3. PRIME NUMBERS. THE SIEVE OF ERATOSTHENES................... 10
~ 4. THE NUMBER OF PRIMES IS INFINITE.............................. 12
~ 5. THE FUNDAMENTAL THEOREM OF EUCLID........................... 13
~ 6. DIVISIBILITY BY A PRIME NUMBER................................ 3
~ 7. THE UNIQUE FACTORIZATION THEOREM............................ 14
~ 8. THE DIVISORS OF AN INTEGER.................................... I6
~ 9. THE GREATEST COMMON FACTOR OF Two OR eMORE INTEGERS....... IS
~ IO. THE LEAST COMMON MULTIPLE OF TWO OR e MORE INTEGERS........ 20
~ II. SCALES OF NOTATION............................................ 22
~ 12. HIGHEST POWER OF A PRIME p CONTAINED IN 1!.................. 24
~ i3. REMARKS CONCERNING PRIME NUMBERS........................... 28
CHAPTER II. ON TEI IXNDICATOR OF AN INTEGER
~ 14. DEFINITION. INDICATOR OF A PRIME POWER....................... 30
~ I5. THE INDICATOR OF A PRODUCT..................................... 30
~ I6. THE INDICATOR OF ANY POSITIVE INTEGER......................... 32
~ I7. SUM OF THE INDICATORS OF THE DIVISORS OP A NUMBER............
CHAPTER III. ELEMENTARY PROPERTIES OF CONGRUENCES
~ I8. CONGRUENCES MODULO........................................ 37
~ 19. SOLUTIONS OF CONGRUENCES BY TRIAL...................3.......... 9
~ 20. PROPERTIES OF CONGRUENCES RELATIVE TO DIVISION............... 40
~ 21. CONGRUENCES WITH A PRIME MODULUS........................... 41
~ 22. LINEAR CONGRUENCES........................................ 43
CHAPTER IV. THE THEOREMS OF FERMAT AND WILSON
~ 23. FERMAT'S GENERAL THEOREM.................................... 47
~ 24. EULER'S PROOF OF THE SIMPLE FERMAT THEOREM................. 48
~ 25. WILSON'S THEOREM.............................................. 49
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