Roots of the indicial equation
Verify the origin is regular singularity. Show the roots of the indicial equation do not differ by an integer. Find, by the method of Frobenius, two independent solutions of:
2xy''+(x+1)y'+3y=0
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Let a, b and n be three positive integers with gcd(a,n) = 1 and gcd(b,n) = 1. Show that gcd(ab,n) = 1
Let n > 1. Show that there exists n consecutive composite numbers. (Hint: consider (n+1)!+k for 2?k?n+1, where n!=n*(n-1)* ...2*1)
Determine the center and the radius of each circle:
Write each of the following equation in one of the forms: y=a(x-h)^2+k, x=a(y-h)^2+k, [((x-h)^2/a^2)+((y-k)^2/b^2)=1] or (x-h)^2 +
The ratio for Nacys class is girl to boy 3:5, the ratio of bills class is girl to boy 3:1 is the number of students in Nancys class a multiple of 8? if thetwo classes were combined what would be the new girl:boy ratio?
Whenever multiplying two positive fractions, the product is less than starting numbers? Sometimes? Always? Never? Why?
Describe that given a,b in subset Z and p prime, if neither nor b is the perfect square modul p, then ab is a perfect square modulo p. Hint: for p odd, consider the possible values of a^((p-1)/2) modulo p.
An affine cipher is encryption using simple mathematical function. Suggest the affine cipher c = ax+b (mod 26) where x is the plaintext, the function applied to each letter of plaintext separately, where each letter is represented such as A is 0,
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