2. (a) if ged(a, 35) = 1, show that a = 1 (mod 35). [hint: from fermat's theorem a = 1 (mod 7) and at = 1 (mod 5).] b f ged(a, 42) = 1, show that 168 = 3.7.8 divides aº - 1. (c) if geda, 133) = ged(b, 133) = 1, show that 133 a18 - 18. 3. from fermat's theorem deduce that, for any integer n > 0,131112n+6 +1. 4. derive each of the following congruences: (a) a = a (mod 15) for all a. [hint: by fermat's theorem, a' = a (mod 5).] (b) a' = a (mod 42) for all a. (c)' = a (mod 3. 7. 13) for all a. 9 20) fe

If y varies directly as x2 and y=6 when x=6, find the constant of variation.

The null and alternate hypotheses are: h0: μ1 ≤ μ2 h1: μ1 > μ2 a random sample of 22 items from the first population showed a mean of 113 and a standard deviation of 12. a sample of 16 items for the second population showed a mean of 99 and a standard deviation of 6. use the 0.01 significant level. find the degrees of freedom for unequal variance test. (round down your answer to the nearest whole number.) state the decision rule for 0.010 significance level. (round your answer to 3 decimal places.) compute the value of the test statistic. (round your answer to 3 decimal places.) what is your decision regarding the null hypothesis? use the 0.01 significance level.

What are the solutions of the equation x4 + 6x2 + 5 = 0? use u substitution to solve.