DP Further Mathematics HL Questionbank

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Directly related questions

• 16M.1.hl.TZ0.10a: Show that \({2^n} \equiv {( - 1)^n}(\bmod 3)\), where \(n \in \mathbb{N}\).
• 17M.1.hl.TZ0.11a.i: Without attempting to draw \(J\), verify that J satisfies the handshaking lemma;
• 17M.1.hl.TZ0.2b: Hence find the smallest value of \(x\) greater than 100 satisfying the linear congruence...
• 11M.2.hl.TZ0.4b: (i)     Solve \(17x \equiv 14(\bmod 21)\) . (ii)     Use the solution found in part (i) to find...
• 10M.1.hl.TZ0.4: Given that \({n^2} + 2n + 3 \equiv N(\bmod 8)\) , where \(n \in {\mathbb{Z}^ + }\) and...
• 09M.1.hl.TZ0.6c: Show that \(\sum\limits_{n = 1}^{100} {n! \equiv 3(\bmod 15)} \) .
• 09M.2.hl.TZ0.3B.a: Given that the integers \(m\) and \(n\) are such that \(3|({m^2} + {n^2})\) , prove that \(3|m\)...
• 09M.2.hl.TZ0.3B.b: Hence show that \(\sqrt 2 \) is irrational.
• 08M.2.hl.TZ0.1B.b: Hence solve the simultaneous linear congruences\[3x \equiv 4(\bmod 5)\]\[5x \equiv 6(\bmod...
• 12M.2.hl.TZ0.2B.a: Find the smallest positive integer \(m\) such that \({3^m} \equiv 1(\bmod 22)\) .
• 12M.2.hl.TZ0.2B.b: Given that \({3^{49}} \equiv n(\bmod 22)\) where \(0 \le n \le 21\) , find the value of \(n\) .
• 12M.2.hl.TZ0.2B.c: Solve the equation \({3^x} \equiv 5(\bmod 22)\) .
• 14M.1.hl.TZ0.15: (a)     Show that the solution to the linear congruence \(ax \equiv b(\bmod p)\), where...