Algebraic inequalities by Vasile Cirtoaje

By Vasile Cirtoaje

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Example text

There is, therefore, a mistake in the multi­ plication above. Let's try the other one : 2,749 X 75,812 5 208,407,188 2 4 The numbers 2749 and 75,812 have the digit sums THE PERILS OF DIVISION JUST as subtraction is the reverse of addition, so divi­ of 4 and 5 respectively, as before. The new product, sion is the reverse of multiplication. Since we know 208,407,188, can be simplified by casting out 2 + 7 and 1 + 8, and now, ignoring the zeros, we sum the digits 8 + 4 + 8 = 20 and 2 + 0 = 2. As far as the digit sums are concerned, we have 4 X 5 = 2.

The numbers divisible by o 10 20 2 12 22 4 2 turn out to be: 6 16 26 14 24 0, 2, 4, 6,or 8 is included in the list, as far as you care to carry the list. These numbers are the "even numbers" and they are called that because they are evenly di­ visible by 2. We learn to tell the even numbers at quite an early age. H I were to state the rule that all even 2 you would have no trouble in that respect afterward. 1, 3, 5, 7, 9 are not even numbers. Neither is any larger number that ends in one of those digits.

So are 11, 13, 17, 19. It might seem to you that as numbers get larger and larger, the number of factors they possess increase, be­ cause there are more and more smaller numbers to serve as possible factors. This is true for some numbers, such as 10, which has two factors, 12, which has four factors, and 60, with 10 factors. However, no matter how far you go in the number scale, there will always be numbers with very few fac­ tors; and there will be primes, too - numbers with no factors at all but themselves and 1.

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