Question
Download Solution PDFनिम्नलिखित में से कौन-सी संख्या \((49^{15} - 1) \) का भाजक है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\((49^{15} - 1) \)
प्रयुक्त अवधारणा:
an - bn, (a + b) से विभाज्य है जब n एक सम धनात्मक पूर्णांक है।
यहां, a और b अभाज्य संख्या होनी चाहिए।
गणना:
\((49^{15} - 1) \)
⇒ \(({(7^2)}^{15} - 1) \)
⇒ \((7^{30} - 1) \)
यहाँ, 30 एक धनात्मक पूर्णांक है।
अवधारणा के अनुसार,
\((7^{30} - 1) \), (7 + 1) अर्थात् 8 से विभाज्य है।
∴ 8, \((49^{15} - 1) \) का भाजक है।
Last updated on Jun 10, 2025
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