Find all solutions of the following equation: 24x ≡ 6 (mod 81).
Find the number of solutions in integers to x1 + x2 + x3 + x4 = 12 satisfying 0 ≤ x1 ≤ 4, 0 ≤ x2 ≤ 5, 0 ≤ x3 ≤ 8, 0 ≤ x4 ≤ 9.
Solve the recurrence relation 9an=6an−1−an−2+5n2 with initial conditions a0=1, a1=2.
Given examples of relation on {1, 2, 3, 4} having the properties specified in the following: (a) reflexive, antisymmetric, and not transitive, (b) not reflexive, not symmetric, and transitive.
Show that K5 is not planar?
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