By Katz N.M.

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**Additional info for A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982)**

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Hence The highest common factor (HCF) of each of the three terms comprising the numerator and denominator is xy. Dividing each term by xy gives: x2y x2y x y2 − x y = a 3+(1/2)b(1/2)+(2/3)c(5/2)+3 = a 7/2 b7/6c11/2 x xy = y−1 x y2 x y − xy xy Problem 16. Simplify: ( p3 )1/2 (q 2 )4 a 7/2b7/6c11/2 = a7 6 7 √ 6 b7 c11 1 When a = , b =64 and c = 1, 4 a7 6 1 4 b7 c11 = = 1 2 647 √ 111 7 (2)7 (1) = 1 Using the third law of indices gives: p 3×(1/2) 2×4 q Problem 17. Simplify: (3/2) 8 =p q (mn 2 )3 (m 1/2 n 1/4 )4 The brackets indicate that each letter in the bracket must be raised to the power outside.

50, evaluate the distance 17. The area,√A, of any triangle is given by A = s(s − a)(s − b)(s − c) where a+b+c . 20 cm 18. com/cw/bird This Revision test covers the material contained in Chapters 1 to 4. The marks for each question are shown in brackets at the end of each question. 1. 2. 3. 69 m long, is cut into three pieces in the ratio 2 to 5 to 6. 3 (a) correct to 4 significant figures (2) 5. 15 m, correct to 3 significant figures (3) 6. Evaluate the following: (c) (e) 7. 3 2 −1 −2 2 3 − 1 (d) (27)− 3 2 9 2 8.

E. 3247 correct to 4 decimal places. ) (By calculator, Now try the following Practice Exercise Practice Exercise 16 page 658) Errors (Answers on In Problems 1 to 5 state which type of error, or errors, have been made: 1. 21 2. 3. 6 4. 5. For a gas pV = c. 54 m3 then c = 55 836 Pa m3. 274 In Problems 6 to 8, evaluate the expressions approximately, without using a calculator. 6. 3 7. 96 8. 6215031. . 19448653. . 5374, 2 correct to 4 decimal places Problem 6. 01896453 . . 73 decimal places (a) Use of calculator The most modern aid to calculations is the pocket-sized electronic calculator.

### A conjecture in arithmetic theory of differential equations (Bull. Soc. Math. Fr. 1982) by Katz N.M.

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