...is r, any whole number when divided by r + l will leave the same remainder as the difference between the sum of the digits in the odd places and the sum of the digits in the even places leaves when divided by r + 1. With the same notation as in the preceding proposition we have + .........

...that any whole number when divided by (r + l) will leave the same remainder as the difference between the sum of the digits in the odd places and the sum of the digits in the even places leaves, when divided by (r+1). Express 240'25 in the scale whose radix is (8) and extract the square...

...digits is divisible by 9. 10, when they have 0 in the units' place. 11, when the difference between the sum of the digits in the odd places and the sum of the digits in the even places is either 0, or is divisible by 11. 12, when the two right-hand digits are divisible by 4, and the...

...that any whole number when divided by rf 1 will leave the same remainder as the difference between the sum of the digits in the odd places and the sum of the digits in the even places, when divided by r+1. R (2) Express 240-25 in the scale whose radix b 8, and extract the square root...

...divided by 3. It appears from Art. 445 that a number is divisible by 11 when the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divisible by 11. 447. From the property of the number 9, mentioned in the preceding Article, a rule...

...-remainder 2 2-5«68 4 4- remainder 2 4 4 1- remainder 0 ret 28 (5) by 11 if the difference between the sum of the digits in the odd places and the sum of those in the even places be divisible by 11. 8. If N be a number in the scale whose radix is r, and...

...A number whose radix is r is divisible by r + 1, when the difference between the sum of the diyits in the odd places and the sum of the digits in the even places is so divisible. We have + Рз ('-3 + 1) + 1h (r - 1) + 1h (r + 1) + {Po - 1\ + Pi - Pi + ...- + (-...

...divided by r - 1. 218. A number whose radix is r is divisible Ъу г + 1, when the difference between the sum of the digits in the odd places and the sum of the digits in the even places is so divisible. We have ^=^я_1г"-1+^я_:,гя-2+ ---- +pj*+ptrí+p1r+pl¡...(l). + - Pi + PÍ -...

...the sum of the digits is divisible by 9. 10 when the last digit is o. 11 when the difference between the sum of the digits in the odd places, and the sum of the digits in the even places, is o or a multiple of n. 12 when it is divisible by 3 and 4. Thus the number 51480 is divisible by...

...of notation in which the radix is r any whale number is divided by r + 1, and the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divided by r + 1 ; shew that the remainder will be equal or their sum will be r+ 1. ANSWERS TO JANUARY...