# An Elementary Investigation of the Theory of Numbers: With Its Application to the Indeterminate and Diophantine Analysis, the Analytical and Geometrical Division of the Circle, and Several Other Curious Algebraical and Arithmetical Problems

J. Johnson, 1811 - 507 σελίδες

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### Περιεχόμενα

 I v II 7 III 32 IV 52 V 79 VI 123 VII 153 VIII 176
 X 200 XI 220 XII 261 XIII 317 XV 345 XVI 396 XVII 434 XIX 460

 IX 187
 XX 479

### Δημοφιλή αποσπάσματα

Σελίδα 43 - Euler ascertained, that 231 — 1 = 2147483647 is a prime number; and this is the greatest at present known to be such, and, consequently, the last of the above perfect numbers, which depends upon this, is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for, as they are merely curious without being useful, it is not likely that any person will attempt to find one beyond it.
Σελίδα 477 - Find two numbers whose" product is equal to the difference of their squares, and the sum of their squares equal to the difference of their cubes.
Σελίδα 84 - If a square number terminate with an odd digit, the last figure but one will be even ; and if it terminate with any even digit, except 4, the last figure but one will be odd. 27. No square number can terminate with two equal digits, except two ciphers or two fours, 28.
Σελίδα 23 - ... if a square number be either multiplied or divided by a number that is not a square, the product or quotient is not a square.
Σελίδα 7 - The sum or difference of two odd numbers, is even ; but the sum of three odd numbers, is odd. 4. The sum of any even number of odd numbers, is even ; but the sum of any odd number of odd numbers, is odd. 5. The sum, or difference, of an even and an odd number, is an odd number.
Σελίδα 1 - An EVEN NUMBER is that which can be divided into two equal whole numbers.
Σελίδα 216 - I have been the first to discover a most beautiful theorem of the greatest generality, namely this: Every number is either a triangular number or the sum of two or three triangular numbers; every number is a square or the sum of two, three, or four squares...
Σελίδα 83 - If a square number terminate with a 4, the last figure but one (towards the right hand) will be an even number. 25. If a square number terminate with 5, it will terminate with 25. 26. If a square number terminate with an odd digit, the last figure but one will be even ; and if it terminate with any even digit, except 4, the last figure but one will be odd. 27.
Σελίδα 19 - If an odd number divides an even number, it will also divide the half of it 11. If a number consist of many parts, and each of those parts have a common divisor d, then will the whole number, taken collectively, be divisible by d. 12. Neither the sum nor the difference of two fractions, which are in their lowest terms, and of which the denominator of the one contains a factor not common to the other, can be equal to an integer number.